Solving second order ODEs

AIM To simulate an axi-symmetric flow by applying the wedge and symmetry boundary conditions at various angles in openfoam. THEORY  Here, a pipe of diameter of 20mm is considered. The flow is assumed as laminar and flows through a constant cross-section pipe at an inlet Reynold's number of 2100. Fluid is considered…

AIM To simulate an axi-symmetric flow by applying the wedge boundary condition in openfoam. THEORY  Here, a pipe of diameter of 20mm is considered. The flow is assumed as laminar and flows through a constant cross-section pipe at an inlet Reynold's number of 2100. Fluid is considered as water. Density of water = 1000…

AIM To derive and write a program for in MATLAB for fourth order approximation for second order derivative using central difference, skewed right-sided difference, and skewed left-sided difference schemes. SCHEMES EQUATIONS AND COEFFICIENTS VALUES 1. Central Difference Scheme The order of accuracy P = Number of nodes…

AIM To clean up the given model and perform first, surface meshing and then to perform volumetric meshing for the revelent volume. PROCEDURE The first step is to import the geometry and run a geometry check. Using the geometry check, all the surfaces that need to be fixed (single cons, triple cons, overlapping features)…

CODE:  % Forward kinematics of a 2R robotic arm manipluator clear all close all clc l1 = 1.5; % length of link1 l2 = 1; %length of link2 theta1 = linspace(0,90,25); %angle of 1st rotational joint with x axis theta2 = linspace(0,90,25); %angle of 2nd rotational joint with x axis ct = 1; % for frame counter for i=1:length(theta1)…

Genetic Algorithm  Genetic Algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired…

AIM To clean up the given model and perform first, surface meshing got the given mesh lengths and then to perform volumetric meshing for revelent volumes. PROCEDURE The first step is to import the geometry and run a geometry check. Using the geometry check, all the surfaces that need to be fixed (single cons, triple cons,…

AIM To mesh the given model using triangluar mesh with a target length of 5mm, 3mm, and 1mm. PROCEDURE First, import the given model. Now, we have to clean up the geometry. A geometry check is run to see all single cons and any other errors. These single cons need to be converted to double cons. Under topo module, using…

Specific Heat (J/Kg K) It is the quantity of heat required to raise the temperature of one gram of a substance by one Celsius degree. The units of specific heat are usually calories or joules per gram per Celsius degree. k Enthalpy (J) It is the sum of the system's…

PROCEDURE REPORT - Stock Bracket Top down approach is followed here. An assembly design window is opened and a new part is added. The sketch of a part is created and then the part itself is created using pad, pocket, etc. The same procedure is followed for all 8parts. All 8 parts are individually saved. This can be done…

Code and Result Explaination:  Used ode45 to solve simple pendulum equation under damping. Function - 'ode_func' gives values of dtheta1/dt and dtheta2/dt into the ode 45 solver. this is done since the equation is 2nd order and needs to be reduced to 1st order ODE. Using for loop and we find the position of pendulum…

PROCEDURE REPORT - Radial Engine assembly Top down approach is followed here. An assembly design window is opened and a new part is added. The sketch of a part is created and then the part itself is created using pad, pocket, etc. The same procedure is followed for all 10 parts. All 10 parts are individually saved. This…

PROCEDURE REPORT - Motor Blower Top down approach is followed here. An assembly design window is opened and a new part is added. The sketch of a part is created and then the part itself is created using pad, pocket, etc. The same procedure is followed for all 6 parts. All 6 parts are individually saved. This can be done…

AIM To clean up the given car model and perform first, surface meshing for the given mesh lengths and to create a wind tunnel around the car with surface mesh and volumetric mesh for volume in the tunnel surrounding the car. PROCEDURE The first step is to import the geometry and run a geometry check. Using the geometry…

AIM To clean the topo of the given engine, gearbox and transmission models, merge them and create a surface wrap around them with mesh element target length as 3mm. PROCEDURE After opening the given model files, using the tools under the topo deck, clean the exterior of the engine, gearbox, and transmission. Since the…

AIM To solve for the given 2D heat conduction with the given boundary conditions THEORY The 2D heat conduction equation is given by:  `(deltaT)/(delta t) - alpha ((delta^2T)/(delta x^2)+(delta^2T)/(delta y^2))=0` `alpha`= Thermal Diffusivity. It is considered as 1.5 for our problem. Two main approaches are used. They…

PROCEDURE REPORT - V Block Top down approach is followed here. An assembly design window is opened and a new part is added. The sketch of a part is created and then the part itself is created using pad, pocket, etc. The same procedure is followed for all 3 parts. All 3 parts are individually saved. This can be done using…

Finite Volume Method (FVM) The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using…

AIM To simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle for conservative and non-conservative from of governing equations using MacCromack’s method. THEORY A convergent-divergent nozzle converts subsonic flow at inlet into supersonic flow at outlet.   We consider a steady-isentropic…

AIM To simulate a incompressible-laminar-viscous flow through a backward facking step in openfoam with mesh grading factor of 1 and 0.2. SIMULATION SETUP 1. First we copy the tutorial similat to our case to run file. The cavity tutorial under incompressible>icoFoam>cavity is the case which is similar to what we are…