COMPARISON OF ERROR USING DIFFERENT SCHEMES FOR A SECOND ORDER DERIVATIVE using MATLAB

AHMED BODY: Ahmed body was created by S.R. Ahmed in 1984. Ahmed body is the benchmark model for aerodynamics simulation tool. Ahmed body represents the simplified ground vehicle geometry of a bluff body type. Its shape is simple enough for accurate flow simulation and retains some important practical features…

Gear Sloshing effect: Aim: To perform four simulations of the gearbox sloshing effect and compare the results among all the cases.   Case 1. 20% Immersion, Fluid - Engine oil Case 2. 30 % Immersion, Fluid - Engine oil Case 3. 20% Immersion, Fluid - n-heptane-liquid(c7h16) Case 4. 30 % Immersion,…

When does an ODE become unstable? When the discretization points are too less while discretizing an ODE over a domain, the ODE may become unstable For a time marching solution, the explicit scheme leads to instability when the discrete time steps is large How does stability affect engineering simulations? In engineering…

Objective: To model & simulate the working of the Valve train of an Internal combustion engine using SOLIDWORKS The parameters for the simulation are: Angular velocity of cam: 1500 RPM Material of all components: Cast Carbon Steel The simulation is to be carried out for two different cases of Cam lift: Case 1: Cam…

Aim: To simulate the workspace of a 2-D Robotic Arm using MATLAB Methodology: A 2-D Robotic Arm consisting of two links and an end manipulator is considered. The motion of the links are such that the link at the fixed end is initially given a small angular displacement and the second link completes its angular motion in…

Objective: To simulate the motion of Planetary Gear using SOLIDWORKS Procedure: The Pitch circle diameter and number of teeth is measured for the planetary gear by inspecting the dimensions (No. of Teeth = 16, Pitch circle diameter = 40 mm) The Sun gear, Planetary gears & Ring gear are imported from the SOLIDWORKS…

Objective: To simulate the motion of a piston assembly using SOLIDWORKS Using motion simulation tool in SOLIDWORKS, the working of a Piston Assembly is simulated The results should include the displacement of the Piston head with respect to time for three different cases A piston assembly contains the following components:…

Objective: To simulate the Internal geneva mechanism Procedure: The individual components of driver and driven of the geneva mechanism were created The assembly of the mechanism was formed from applying proper mating The motion study of the mechanism was conducted and results like contact force and driven's angular displacement…

clear all close all clc a_c=-0.08333; b_c=1.333; c_c=-2.5; d_c=1.333; e_c=-0.08333; a_r=2.917; b_r=-8.667; c_r=9.5; d_r=-4.667; e_r=0.9167; a_l=2.917; b_l=-8.667; c_l=9.5; d_l=-4.667; e_l=0.9167; x=1; dx=0.025; function [ydot]=f(x); ydot=zeros(1,1); ydot(1)=exp(x)*cos(x); end f_exact=exp(x)*(-sin(x)+cos(x)); f_fds =(f(x+2*dx)-2*f(x+dx)+f(x))/(dx^2);…

CODE FOR STEADY STATE CONDUCTION: Four iterative solvers are used for steady state condction. The jacobi solver doesnot takes the previously updated values whereas gauss siedel solver considers the previously updated value of node while calculating the temperature for the next node. Hence gauss siedel iterative solver…

CHT ANALYSIS: The term conjugate heat transfer is used to describe processes which involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids. A typical example is the heating or cooling of a solid object by the flow of air in which it is immersed. CHT helps in…

MODEL: The processor of 6.4 W is used for analysis. Heat generation value will be 10^8 W/m^3 as total volume of the processor is 64mm^3 The material used for each components are: processor- gold fins- copper and PCB of aluminium The air with 5 metre per second is allowed to pass over fins at 300 K .The k-epsilon model…

SOME PRACTICAL CFD MODELS BASED ON RAYLEIGH TAYLOR WAVES: 1. The Richtmyer–Meshkov instability (RMI): The Richtmyer–Meshkov instability (RMI) occurs when two fluids of different density are impulsively accelerated. Normally this is by the passage of a shock wave. The development of the instability begins with…

GATE VALVE MODEL: The gate valve geometry is imported in spaceclaim VOLUME EXTRACTION: Volume is extracted by selecting relevant edges and aplying volume extract command. The fluid volume is then pulled outside to a certain distance   DESIGN POINTS: GATE DISC LIFT VARIATION 1. 10mm 2. 15mm 3. 20mm 4. 25mm 5.…

The four emperical models used for cyclone separator efficiency are: 1. Koch and Licht model 2. Lappel model 3. Li and Wang model 4. Iozia and Leith model IOZIA AND LEITH MODEL Iozia and leith logistic model is developed based on force balance. The model assumes that a aprticle carried by a vortex endures the influence…

Combustion Simulation in FLUENT: Based on mixing: 1. Non-premixed combustion: Example- direct injection of fuel in a CI engine where the air is first sucked and compressed and fuel is directly injected into the engine at the end of compression stroke. Materials are initially Non-premixed 2. Premixed combustion: Materials…

Recuperator: A form of heat exchanger in which hot waste gases from a furnace are conducted continuously along a system of flues where they impart heat to incoming air or gaseous fuel.   1. Effect of pre-heating on Adiabatic Flame Temperature Combustion of Methane: `CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2` Range of pre-heating…

Known: Fluid: Water Reynolds number: 2100 Density: 997 kg/m3 Kinematic viscosity: 1.004e-6 m2/s OpenFOAM solver to be used: IcoFoam Assumption: diameter: 10mm Flow is incompressible, irrotational and laminar Calculation of Length of pipe: L=Le+0.3 Le= 0.06*Re*D=1.26m L=1.56m Calculation of Average and Maximum velocity:…

OBJECTIVE: To use the icoFOAM solver to simulate the flow through a backward-facing step, creating multiple meshes comparing the results obtained from each mesh. MESH SPECIFICATIONS: Number of cells along the x-direction (longer dimension) = 200 Number of cells along the y-direction = 10 Use a graded mesh. The grading…

Known: Fluid: Water Reynolds number: 2100 Density: 997 kg/m3 Kinematic viscosity: 1.004e-6 m2/s OpenFOAM solver to be used: IcoFoam HAGEN-POISEUILLE FLOW: In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law…

Finite volume method uses an integral approach to solve complex governing differential equations related to the problem. It uses gauss divergence theorem to convert volume integral to a surface integral Need for gradient and interpolation schemes: Gradient and interpolation schemes are needed when an estimate of an unknown…

AIM: To solve the given Stiff ordinary differential equations employing implicit/BDF and solving by Multivariate Newton-Raphson method `(dy1)/dt = -0.04*y1 + 10^4*y2*y3` `(dy2)/dt = 0.04*y1 - 10^4*y2*y3 - 3*10^7*y2^2` `(dy3)/dt = 3*10^7*y2^2`   Employing BDF (backward differencing)/ Implicit method to the ODE\'s we…

Aim: To write a code from GRI mechanism for the combustion of Methane  and to calculate 10 most sensitive reactions with respect to Temperature Objectives: 1. Plot the variation of Temperature and Molar concentration of different species w.r.t. time 2. Plot a bar graph showing most Sensitive reactions w.r.t. temperature…

Objective: Performing simulation on Reaction Reduction Mechanism for the GRI 3.0 mechanism Run a reference ignition delay and maximum temperature analysis for the unlowered function for a time duration Consequently, a temperature sensitivity analysis should be performed on all system reactions and the reactions should…

Aim: To calculate the global maxima of a stalagmite function Introduction: A genetic algorithm is a search heuristic that is inspired by Charles Darwin's theory of natural evolution. This algorithm reflects the process of natural selection where the fittest individuals are selected for reproduction in order to produce…

Objective: To create a Rankine cycle simulator using MATLAB The rankine cycle as shown in the figure below, consists of the following processes:   1-2: Isentropic compression in the pump 2-3: Constant pressure heat addition in the boiler 3-4: Isentropic expansion in the turbine 4-1: Constant pressure heat rejection…

Objective: Write a program to solve an ODE representing the motion of a Simple Pendulum Equation for the motion of a simple pendulum: `(d^2(theta))/dt^2+b/m*(d(theta)/dt)+(g/l)*sintheta=0` Pendulum characteristics: Length = 1 meter mass = 0.1 kg b = 0.1 gravity = 9.81 m/s^2 The motion is analysed for a totle time of 20…

Objective: To write a function that extracts the 14 coefficients from NASA thermodynamic data file and calculates the enthalpy, entropy and specific heats for all the species in the data file NASA  came up with polynomials that can be used to evaluate thermodynamic properties such as Cp, H and S. They have also…

AIM: To write a code to calculate auto-ignition time for combustion of Methane under different operating conditions using cantera Case 1:Plotting the variation of Auto Ignition time of Methane with a constant temperature of 1250 K and pressure varying from 1 to 5 atm Case 2: Plotting the variation of Auto Ignition…

Aim: To derive the reaction rate ODEs of a simple reaction mechanism   `CO + O2 implies CO2 + O` `O + H2O implies OH + +OH` `CO + OH implies CO2 + H` `H + O2 implies OH + O` Compact Notations: Matrix form for reactants: `v\'ji = [[1,0,0,0,0,1,0],[0,1,1,0,0,0,0],[0,0,0,0,1,1,0],[1,0,0,1,0,0,0]]` Matrix form for…

Handling Mixtures with Cantera `CH4+2(O2+3.76N2)=CO2+2H2O+7.52N2` 1.  Using the \"moles\" method/function of the A object and explaining how it was calculated. You need to use this after line number 9. For combustion of 1 mole of methane 2 moles of air are required 1 mole of air contains 0.21 mole of Oxygen Combustion…

Adiabatic Flame Temperature: The adiabatic flame temperature for a given fuel oxidizer combination is determined by finding the final state temperature or the adiabatic flame temperature for which the sum of the enthalpies of the reactants equals the sum of the enthalpies of the products To calculate it theoretically we…

Matlab Code for Conservative Form: %Conservative form clear all; clc all; close all; n=61; x=linspace(0,3,n); dx=x(2)-x(1); gaamma=1.4; c=0.5; %cfl number e=10e9; tol=10e-4; %convergence criterion a=1+2.2*(x-1.5).^2; %Initial conditions for i=1:n if (x(i)<=0.5) rho(i)=1;t(i)=1; elseif (x(i)>=0.5 && x(i)<=1.5)…