Transient Behavior of a Simple Pendulum using MATLAB

PROBLEM STATEMENT: 1. Steady state analysis & Transient State Analysis Solve the 2D heat conduction equation by using the point iterative techniques that were taught in the class. The Boundary conditions for the problem are as follows; Top Boundary = 600 K Bottom Boundary = 900 K Left Boundary = 400 K Right Boundary…

INTRODUCTION: A multiphysics problem exhibits certain characteristics that are helpful for simulations. The two dimensional Navier Stokes Momentum Equation is given by the formula:                                        …

INTRODUCTION: A multiphysics problem exhibits certain characteristics that are helpful for simulations. The two dimensional Navier Stokes Momentum Equation is given by the formula:                                        …

OBJECTIVE: To solve the ODE which represents the equations of motion in a simple pendulum with damping by writing MATLAB code.  To simulate the motion of a simple pendulum with damping with MATLAB code. MATHEMATICAL FORMULATION: The ODE is of 2nd order which represents the equations of motion in a simple pendulum…

INTRODUCTION: Numerical Solution can only give answers at discrete points in the domain which are called as grid points. The finite difference methods is for replacing the partial derivatives appearing in governing equations of fluid dynamics, with algebraic difference quotients yielding a system of algebraic equations…

PROBLEM STATEMENT: Write a Reaction Reduction Mechanism code for the GRI3.0 mechanism, Your code should do the following, First, it should run a reference Ignition delay and Max temperature Analysis for the unreduced mechanism for a set of state values (Temperature, Pressure and Equivalence ratio) for a time duration of…

FLAME SPEED ANALYSIS   THEORY: Flame Speed tells us how fast the flame diffuses i.e. When we ignite the flame at one point how soon the flame propagates and reaches the other end. The reaction properties alone for the flame are not important, we consider the diffusion properties as well. When the species diffuses…

INTRODUCTION: Coupled Non Linear ODE\'s are solved to get the reaction mechanisms and we integrate a set of ODE\'s to get the Ignition Delay. Ignition Delay is sensitive to all the reaction parameters. Some reactions are more sensitive and some reactions are less sensitive to the ignition delay. Sensitivity Analysis is…

When does a ODE become unstable? Increments of time and space appear throughout the differential equations. Stability is achieved for the Explicit approach problem by limiting the value of time increment(Δt) for a particular value of space increment(Δx). If the value of Δt is larger than the limit imposed…

The stoichiometric combustion of Methane is shown as follows: CH4 + 2 [O2 + 3.76 N2] → CO2 + 2H2O + 3.76N2 1. Use the \"moles\" method/function of the A object and explain how it was calculated ? An object A is created where we assign values for the oxidizer. It is at initial conditions of Temperature(298.15K) and…

EFFECT OF EQUIVALENCE RATIOS ON THE ADIABATIC FLAME TEMPERATURE:- 1. ADIABATIC FLAME TEMPERATURE: Let us assume a mixture of fuel and air in a particular system. Combustion happens because of the chemical reaction between the Methane and air. The fuel and air are not allowed to leave the system i.e. Heat Transfer is not…

DEFINITIONS:-INITIAL CONDITIONS: 

The following results can be concluded for the two different plots: 1. In the first plot the drag force varies slightly in a parabolic path with an increase in velocity and then the curve is linear. The variation can be depicted in  a graph. The same kind of variations can also be expected from the drag force if the…

The multistep reaction mechanism is given below: We have 8 species and 4 reactions for the given reaction mechanism.  Now we have to represent the species and the reactions in terms of a compact notation. The node j represents the species which are listed as a table shown down below: j 1 2 3 4 5 6 7 Species H O CO…

INTRODUCTION: 1) AUTO IGNITION: The lowest temperature we require to heat up an air-fuel mixture in a chamber is referred to as Auto-Ignition. Most fuels don\'t burn at the room temperatures, so we need an ignition source which represents the exact conditions for combustion to happen. Auto-Ignition can indicate the right…

Literature review RANS derivation and analysis 1.1 INTRODUCTION RANS stands for Reynolds Averaged Navier Stokes equation. They are used to create turbulence models for studying engineering simulations. In R&D they are used for flow based analysis. Here we solve equations for Ensemble Averaged Velocity Fields. i.e.…

The following program is used for simulating the motion of a Robotic Arm based on the principle of Forward Kinematics which is responsible for computing the position of the end-effector from specified values for the joint parameters. The kinematics equations of the robot are used in robotics, computer games, and animation.…

HEAT RECUPERATOR: A furnace is used for burning the air and fuel mixture. When it burns it releases a lot of energy and converted to work. This energy is harnessed by a work harvesting device which can be a turbine as well, we get flue gases which are energy rich and enthalpy rich as well. We put the heat exchanger to…

INTRODUCTION: The Newton-Raphson method discussed above for solving a single-variable equation  can be generalized for solving multivariate equation systems. A stiff ODE is the one where we use implicit methods to integrate the particular system consisting of non linear equations. The particular ODE\'s shown below…

TYPES OF TURBOCHARGER: Single Turbo Sequential Turbos Twin Scroll Turbo  Variable Geometry Turbo Variable Twin Scroll Turbo Electric Turbo TURBOCHARGER EXAMPLES IN GT-POWER: The model given below is an example of a twin scroll turbine modelled using GT Power: In the model shown above we have two entries for a single…

OBJECTIVE: To do thermodynamic analysis of an engine which can be used for tractor applications for use in India and has to comply with a minimum BSFC target of 210 g/kW-h and a maximum BSFC target of 225 g/kW-h. MODEL DESCRIPTION: The model of TAFE 7502 DI 4WD at a system level is based on the configuration described…

INTRODUCTION: A model of a compression ignition engine running at 1800 rpm is given below: Air is allowed to enter through the inlet and moves along the runners to meet at the throttle and then allowed to enter the cylinder. Fuel is injected directly into the cylinder for combustion to happen and exhaust gases are allowed…

OBJECTIVE: To do a case study on an Honda SI Engine F20C variant and to run the setup in GT-Power for Maximum Power and Maximum Torque conditions and get the key performance graphs. ENGINE SPECIFICATIONS: Four cylinder DOHC (Dual Overhead Camshaft) 16 valves (87mm*84mm) 4 valves/cylinder i.e. Two intake and two exhaust…

INTRODUCTION: A spark ignition model of an IC Engine being taken for our case setup is a single cylinder model where fuel is injected through the ports and the mixture of air and fuel enters the cylinder for combustion to happen. This model of our engine runs at 1800 RPM and the key parameters are noted down.   …

1. INTRODUCTION: GT Suite is a multiphysics CAE system simulation software.The foundation of GT-SUITE is a versatile multi-physics platform for constructing models of general systems based on many underlying fundamental libraries: Flow library (any fluid, gas or liquid or mixture) Acoustics library (both non-linear and…

OBJECTIVE: To compare the emissions such as NOx, Soot and Unburnt Hydrocarbons as well as key performance parameters for an Open W Piston vs an Omega Piston in Diesel Engines. PROCEDURE:- 1.1 INTRODUCTION: A typical diesel engine consists of a piston, liner and a cylinder head. The type of simulation we are going to run…

OBJECTIVE: To run a full hydro simulation using Converge CFD and also get all the performance parameter graphs. PROCEDURE:- 2.1 QUESTION AND ANSWERS 2.1.1 COMPRESSION RATIO A compression ratio is a ratio where you’re compressing the maximum cylinder volume into the minimum cylinder volume. That’s the volume…

OBJECTIVE: To run a full hydro simulation using Converge CFD and also get all the performance parameter graphs. 1.1 INTRODUCTION When fuel injection takes place due to the interaction of the liquid with the surrounding air there is a drag force which causes disturbances in liquid length. These disturbances propagate and…

OBJECTIVE: To perform surface preparation and boundary flagging tasks on our IC Engine case and setup a No Hydro simulation. PROCEDURE: When importing our geometry and running the diagnosis in Converge CFD we are prone to get a lot of errors in the design geometry. First we flag recognisable boundaries and hide certain…

SHOCK TUBE DESCRIPTION: A shock tube consists of a low and high pressure regions seperated by a diaphragm. When the diaphragm is broken and since there is no interface the fluid in the high pressure zone is going to enter the low pressure zone. Because of this pressure difference the shock waves develop. For a fuel and…

INTRODUCTION: Conjugate Heat Transfer involves allowing the fluid to flow through a solid pipe and here the solid pipe is heated by an external flux due to thermal interactions at the interface between the solid and fluid. SURFACE PREPARATION: Create two concentric cylinders and remove the front and back faces i.e. cross…

SHOCK WAVE: A shock is a compression wave or thin region across which large gradients of the pressure, temperature, velocity occurs and also the transport phenomena of momentum and energy is considered important. Flow consists of large number of fluid molecules in unit volume and the transport of mass, momentum and energy…

INTRODUCTION: A fluid passes through an elbow channel fitted with a throttle valve allowed to rotate at a particular angle for a particular peroid of time. Because of the movement of a throttle valve the flow that passes through it, gets disturbed which is the basic idea for transient flow simulation. BOUNDARY GEOMETRY:…

Elbow Channel Case Description: Elbow Channel consists of a throttle valve which lies inbetween the inlet and outlet. The throttle valve remains stationery and we are going to visualize the flow distribution near it. The normals are required to be pointed inside the elbow so that fluid is simulated inside the domain. We…