Solving ODE of simple pendulum motion using Octave / MATLAB

Aim:-> To perform discretization of intake manifold with converting it in 1D circuit model from 3D model and observing effect of discretization length on result.    Theory: Discretization is the splitting of large parts into smaller sections to improve a model's accuracy. There are two ways in which a fluid…

Aim:-> Conjugate heat transfer (CHT) analysis of exhaust port. Theory:-  As we know heat is transferred by 3 modes i.e. Conduction, convection & radiation. Conduction:- is an exchange of energy by direct interaction between molecules of a substance containing temperature differences. Convection:- is…

Aim:-> Study of turbocharger and its modeling using GT Suit.   Theory:- A turbocharger (technically a turbosupercharger), colloquially known as turbo, is a turbine-driven, forced induction device that increases an internal combustion engine's power output by forcing…

Aim:-> To compare SI and CI engine and perform basic calibration of single cylinder CI engine.   Comparison of SI V/S CI Engine model: SI Engine CI Engine SI engine is internal combustion engine that operates on the principle of spark ignition. CI engine is internal combustion engine that operates on the principle…

Aim:-> Aftertreatment devices modelling for CI and SI Engines using GT Power.   Theory:  An aftertreatment system is a method or device for reducing harmful exhaust emissions from internal-combustion engines. In other words, it is a device that cleans exhaust gases to ensure the engines meet emission norms…

Aim:-> Thermodynamic analysis of tractor engine Preet 7549 model.   Introduction: A tractor is an engineering vehicle specifically designed to deliver a high tractive effort (or torque) at slow speeds, for the purposes of hauling a trailer or machinery such as that used in agriculture,…

Aim:-> To perform CFD simulation of PFI engine including geometry cleanup, boundary flagging, no hydro simulation and full hydrodynamic simulation.   Theory:- The purpose of typical internal combustion engines is to produce work by converting chemical energy to mechanical energy. In internal combustion engines…

Aim:-> Setting combustion simulation for diesel engine and comparing result between open W piston and omega piston.   Theory:- The purpose of typical internal combustion engines is to produce work by converting chemical energy to mechanical energy. In internal combustion engines chemical energy in the fuel…

Literature review of RANS Model   Reynolds Number:- It is the non-dimensional number, as it is ratio of two similar quantities (force). The Reynolds number is expressed as ratio of inertial force to viscous force within a fluid. The Reynolds number is term, which tells behavior of fluid. As inertial force is less,…

Aim:-> To setting up shock tube simulation using Converge CFD.   Theory:- The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale. Or in simple language shock tubes are devices…

Aim:-> Conjugate heat transfer simulation of pipe using Converge CFD   Theory:- As we know heat is transferred by 3 modes i.e. Conduction, convection & radiation. Conduction:- is an exchange of energy by direct interaction between molecules of a substance containing temperature differences. Convection:- is…

Aim:-> To simulate Prandalt Mayer shock wave problem at various sub grid criterion.   Theory:- Shock wave: A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. A shock wave or shock, is a type of propagating disturbance that moves faster…

Aim:-> To perform transient simulation of flow over throttle body.   Theory:- In a traditional spark ignition gasoline engine, the throttle body is the part of the air intake system that controls the amount of air that flows into an engine's combustion chamber. It consists of a housing unit that contains a…

Aim:-> To compare the result for flow over backward facing step at various mesh sizes.   Theory:- Backward Facing Step (BFS) flow, also called as “sudden expansion flows”, “circular expanding flow”, “back-step flow”, “diverging channel” or “backward flow”.…

Aim:-> To sort reactions present in gri.30 mechanism as per sensitivity then create reduced mechanism using the sorted reactions and finally compare ignition delay and maximum temperature (Adiabatic Flame Temperature) of reduced mechanism with original gri.30 mechanism.   Theory:-  Reaction mechanism:…

Aim:-> To perform 1D combustion flame speed analysis using Cantera and Python coding.   Theory:- Flame:  Flame word is originated from Latin word 'flamma'. A flame is the visible gaseous part of fire generated due to exothermic reaction in very small area. The flame occupies a small portion of the…

Aim:-> To compute sensitivities of various reactions in GRI 3.0 mechanism for methane combustion.    Theory:- As we know any combustion reaction consists of number of intermediate chemical reactions and chemical species before complete combustion takes place which affects the entire reaction process.…

Aim:-> To observe the effect of initial temperature and pressure on ignition delay and ignition temperature using Python and Cantera.   Theory:-  Auto ignition temperature:  In the context of a combustible fuel mixture, the auto-ignition temperature is the lowest temperature at which the fuel will…

Objective:-> To compare velocity profile of square wave between original and final velocity at different number of nodes.   Theory:- We have 1D linear convection as- `(delu)/(delt)+ C(delu)/(delx)=0` The above equation is restricted to 1D only that's why the velocity propagate only in single direction…

Aim:-> To solve ODE's using multivariant Newton Raphson method   Introduction:- The Newton Raphson method is used to get the solutions of nonlinear equations system. The Newton-Raphson method (also known as Newton's method) is a way to find an approximation for the root of a real-valued function…

Objective:- To understand importance of stability in solution for solving ODE's.    Theory:- Differential equation: An ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. And a differential equation…

Objective:- To derive compact notations for chemical reaction mechanism   Rate of reaction:  Reaction rate or a rate of reaction is a term generally used in chemistry which defines the speed at which a chemical reaction proceeds. It is often expressed in terms of either the concentration (amount…

Aim:-> To obtain and compare simulation result with "symmetry" boundary condition and "wedge" boundary condition at different wedge angles (10, 25 & 45 degrees). Theory:- As we are considering circular pipe which is symmetric about central axis so instead of taking whole pipe cross section let us consider wedge…

Aim:-> To simulate flow through the pipe using icoFoam solver in OpenFoam. Theory:- As we are considering circular pipe which is symmetric about central axis so instead of taking whole pipe cross section let us consider wedge (sector) of pipe only. Taking such sector and simulating it by using symmetrical boundary…

Objective:-> To simulate the flow of fluid through backward facing step using icoFoam solver. Mesh specification: Number of cells along the x direction (longer dimension) = 200 Number of cells along the y direction = 10 Number of cells along the z direction = 1 Boundary condition specification: Geometry dimensions…

Aim:-> To perform numerical flow simulation of quasi 1D subsonic-supersonic nozzle using MacCormack technique with conservative and non conservative methods.   Theory:-  MacCormack technique:- MacCormack method is an explicit finite difference technique which is second order accurate in both time…

Aim:-> To observe effect of preheating temperature on adiabatic flame temperature (AFT) and combustion efficiency.   Theory:-  Industrial furnaces are used for carrying out certain processes that require heat. Heat in the furnace is provided by either Chemical energy (like fuels, coals), Electrical energy…

Aim:-> To calculate and observe effect of equivalence ratio, variable heat loss and variation of hydrocarbon species on adiabatic flame temperature (AFT) using python and Cantera. Theory:-  Adiabatic flame temperature (AFT): This temperature is defined as the temperature that is achieved by allowing fuel to…

Aim:-> Combustion simulation on combustor model using ANSYS fluent and to analyze effects of adding water in fuel on pollutants (NOx & Soot) generation. Theory:-  Combustion:  Combustion or burning is a high temperature exothermic chemical reaction between a fuel (hydrocarbons) and an oxidant (air) accompanied…

Aim:-> To perform CFD analysis on cyclone separator. Theory:- Cyclone separator:- It is the separation devices which works on principle of inertia to remove particulate matter from flue gases. Cyclone separators is one of many air pollution control devices, known as pre-cleaners since they generally remove…

Aim:-> To perform parametric study on gate valve simulation in ANSYS Fluent. Theory:- Fig: Gate valve schematic diagram   As shown in above figure, gate valve's main components are body, seat, gate, stem, bonnet, and actuator. The primary operation mechanism is straightforward. Turning the handwheel rotates…

Objective :-> Simulate flow over a cylinder for study of following parameters- Phenomenon of Karman vortex street. To obtain Strouhal number at Reynolds number=100. To compare `C_d` (drag coefficient) for different Reynolds number. Theory:- In fluid dynamics vortex shedding is an oscillating flow that takes…

Aim:-> To perform aerodynamic flow simulation on Ahmed body. Theory:- Ahmed body:-  The Ahmed body is a bluff body or rather a generic car body (a simplified vehicle model). The air flow around the Ahmed Body captures the essential flow features around an automobile and was first defined and characterized in the…

Our objective is to write a program that solves the following ODE. The following ODE represents the equation of motion of a simple pendulum with damping. `(d^2theta)/(dt^2)+b/m (d theta)/dt + g/L sintheta = 0` where,  g = gravity in m/s2, L = length of the pendulum in m, m = mass of the ball in kg, b = damping coefficient.…

Finite Volume Method (FVM):- It is a numerical discretization method for the approximation of a single or a system of partial differential equations (PDEs). These partial differential equations (PDEs) are frequently called as conservation laws. These PDEs may be parabolic, elliptical or hyperbolic in nature.…

Objective:-> To solve the 2D steady and unsteady (Transient) heat conduction equations by using the point iterative techniques. Following iterative technique can be used. Jacobi Gauss-seidel Successive over-relaxation Given data:-  Top Boundary = 600 K Bottom Boundary = 900 K Left Boundary = 400 K Right Boundary…

Aim:-> Conjugate heat transfer analysis on graphic card using ANSYS Fluent. Theory: Conjugate heat transfer (CHT) is a type of simulation where it allows heat transfer between fluid and solid domain by exchanging thermal energy at contact surface. Here heat is exchanged at interfaces and transported by conduction…

Objective:- To compare truncation error values between Central difference scheme, Skewed right-sided difference scheme & Skewed left-sided difference scheme for 4th order approximations of the second-order derivative. Theory:-  A Taylor series is a series expansion of a function about a point.…

Aim:-> To perform gearbox lubrication fluid sloshing simulation using user defined function (UDF) in ANSYS Fluent. Theory:-  Lubrication:- Friction is the force that resists relative motion between two bodies in contact. If friction didn’t exist, nothing would ever stop moving. We need friction to function,…

Our objective is to calculate 'first derivative' of function f(x) at `x=pi/3` by using approximation method (first order, second order and fourth order approximations) at diffrent values of 'dx' . After calculating derivative we have to calculate truncation error for first, second and fourth order approximation…

Aim:-> To understand Phenomenon of Rayleigh Taylor instability using simulation on ANSYS fluent.  Theory:- When a heavy fluid is kept over a light fluid under a gravity or under an external acceleration of the fluid system in the direction toward the denser fluid, the fluid interface becomes unstable. Such…