Week 3.2 - Simulating a 2nd order ODE system of a simple pendulum

Objective: To solve the second order ODE that governs the pendulum using the odeint function, and creating animation of the pendulum. Problem Statement : The differential equations are the equations that are used to predict the behaviour of bodies. And solving them is one of the most important aspect. The governing equation…

Objective: To plot the PV diagram of the otto cycle and compute the thermal efficiency. Python code: import math import matplotlib.pyplot as plt import numpy as np def engine_kinematics(bore,stroke,cr,l,start_angle,end_angle): # to calculate the volume values at different crank angles for compression and expansion processes…

Aim: To run the simulation of a single-cylinder SI Engine at 1800 rpm, to understand and analyze the important parameters, and increase the power output at 3600 rpm by 10%. Problem Statement : 1. Run the case at 1800 rpm and list down important parameters (20 Marks) air flow rate BMEP BSFC In-cylinder pressure 2. Increase…

  Aim: To explore the GUI of GT-Power, locate the listed settings, explore the intercooler tutorial, and solve a problem. Problem Statement : 1. Explore the GUI of GT SUITE and list down modules available with a brief description. (15 marks) 2. Locate the following settings: Time control flag (5 Marks) Time step and…

Aim: To check for geometrical errors, delete unwanted surfaces, merge all three geometries, and create surface wrap on the automotive assembly. Working Methodology : The working methodology that is followed to create surface wrap on any geometry is : 1. Import the geometry. 2. Delete the unwanted surfaces. 3. Close the…

Aim: To check and solve all the geometrical errors, assign relevant PIDs, and perform surface mesh on the cyber truck geometry as well as the wind tunnel surfaces. Working Methodology : The working methodology that is followed to generate mesh on any geometry is : 1. Import the geometry. 2. Check for geometrical errors.…

Aim: To check and solve all geometrical errors on half portion, assign relevant PIDs, and generate a surface mesh on the BMW car geometry and wind tunnel surfaces. Working Methodology : The working methodology that is followed to generate mesh on any geometry is : 1. Import the geometry. 2. Check for geometrical errors.…

Aim :  To check for errors, perform geometry cleanup, and generate a surface mesh and volumetric mesh on the turbocharger. Introduction : A turbocharger consists of a compressor wheel and exhaust gas turbine wheel coupled with a solid shaft that is used to boost the intake air pressure of an internal combustion engine. The…

Aim: To check for geometrical errors, perform topology cleanup and generate surface meshing on the pressure valve. Working Methodology : The working methodology that is followed to generate mesh on any geometry is : 1. Import the geometry. 2. Check for geometrical errors. 3. Geometry cleanup. 4. Assigning relevant PIDs.…

Aim: To see the effect of eigenvalues and spectral radius on the convergence rate while solving the linear system of equations using different iterative methods like Jacobi, Gauss Siedel, and Successive over-relaxation methods. Matlab code: Main code: clear all close all clc % solving the lineaar system of equations ax=b…

Aim :  To solve the one-dimensional linear convection equation which partly resembles the governing momentum equation in Matlab. And to analyze how the solution changes with changing the size of time steps. Matlab code : Writing a function that takes the input argument as the size of the time step to analyze how the…

Aim : To solve the one-dimensional linear convection equation which partly resembles the governing momentum equation in Matlab. And to analyze how the solution changes with changing the number of nodes. MATLAB code : %solving linear convection equation %du/dt + c*du/dx=0 close all clear vars clc %inputs L=1; % length of…

clear all close all clc % solving the governing eqn of a pendulum % d^2(theta)/dt^2 + b/m d(theta)/dt + g/L sin(theta) = 0 %inputs b=0.5; %damping coefficient g=9.8; % acceleration due to gravity m=1; % mass of the ball l=1; % length of the pendulum t= linspace(0,20,1000); % the time interval from 0 to 20s is divided equally…

Aim: To find the stoichiometric coefficient 'ar' and find the relation between the number of carbon atoms 'n' and the stoichiometric coefficient 'ar' for alkanes, alkenes, and alkynes. Problem-solving methodology: Relations between the number of carbon atoms 'n', stoichiometric coeff 'ar', hydrogen atoms 'a', oxygen…

Aim : 1. To perform fluid sloshing simulations in the gearbox to visualize the reach of the fluid over the gear teeth.  2. To implement dynamic meshing methods and user-defined functions for this application. Introduction : Fluid sloshing : In fluid dynamics, slosh refers to the movement of liquid inside…

AIM: 1. To simulate the combustion of natural gas in a combustor. 2. To plot the mass fractions of different species (CH4, O2,  N2, CO2, H2O, NOx, soot). 3. To add water to the fuel and analyze the formation of soot and NOx pollutants. Introduction : Combustion reactions: All combustion reactions fall into the pattern: …

Aim: 1. To perform fluid flow simulation on the gate valve. 2. To parameterize the lift distance from 10mm to 80mm and analyze the mass flow rate at the outlet. Introduction : A gate valve is a control valve that regulates the fluid flow accordingly. The main advantage of a gate valve is the straight-through unobstructed…

Aim : To perform steady-state conjugate heat transfer analysis on a hypothetical graphics card.  Introduction : A graphics card is an expansion card that generates a feed of output images to a display device (such as a computer monitor). At the core is the graphics processing…

Aim : 1. To perform conjugate heat transfer analysis on the Exhaust port. 2. To create inflation layers maintaining the y+ value according to the turbulence model chosen. 3. To perform a validation study. Introduction: The exhaust manifold, which collects engine exhaust gas from multiple cylinders and delivers it to the…

Aim :  1. To simulate the flow through pipe considering an axisymmetric section of the flow by applying the wedge boundary condition.  2. To perform validation studies. Introduction : Fluid flow in circular and noncircular pipes is commonly encountered in practice. The hot and cold water that we use in our homes…

Aim :  To simulate the isentropic flow through a quasi-1D subsonic-supersonic nozzle by solving both conservative and non-conservative forms of the governing equations. Introduction: we consider the steady, isentropic flow through a convergent-divergent nozzle as shown in the below figure. The flow at the inlet to…

Aim: To simulate an incompressible, laminar, viscous flow through a backward-facing step in OpenFOAM and post-processing in Paraview. Introduction : Backward Facing Step (BFS) is widely known for its application in the studies of turbulence in internal flows. The flow separation is caused due to the sudden changes in the…

Aim : 1. To perform analysis on cyclone separator and analyze the efficiency by changing the particle size, and flow velocity (particle velocity). 2. To implement the discrete phase model for this application. Introduction : Cyclone separators or simply cyclones are separation devices that use the principle…

Aim: 1.  To simulate the manipulator's workspace attached to the robotic arm. 2. To create an animation of the simulation. The robotic arm consists of two links. One end of the first link is fixed to the base at (0,0) and rotates about the fixed point. Depending upon the value of theta1(angle made by the link1 with…

Aim : To perform the Rayleigh Taylor instability with various mesh sizes and user-defined fluid to understand the physics behind instabilities and the importance of the Atwood number. Introduction: The instability of a heavy fluid layer supported by a light one is generally known as Rayleigh-Taylor (RT) instability. It…

Aim :  1. To perform external flow simulations over the Ahmed body. 2. To perform a grid independency study. 3. To understand the importance of the Ahmed body and the physics behind it. Introduction : Optimized external car aerodynamics is necessary to achieve efficient vehicles with minimized fuel consumption, CO2…

Aim : 1. To simulate the flow over a cylinder using both steady and unsteady solvers and understand the phenomenon of Karman Vortex Street. 2. To observe and analyze the effect of the Reynolds number on the co-efficient of drag. 3. To understand the convergence criteria. Introduction: External flows past objects have been…

Aim: 1. To perform steady-state simulations to observe the flow field inside the T-junction geometries(both long and short). The reason for this experiment is that, inside the T-junction, due to the different temperatures at inlets(hot and cold inlets), can lead to temperature fluctuations at the adjacent walls. 2. To…

Aim : To solve the 2D heat conduction equation for both steady-state and unsteady-state using iterative solvers using the Jacobi method, gauss seidel method, and successive over-relaxation method for both implicit and explicit schemes Theory : case 1: steady-state analysis, implicit method. The 2D heat conduction equation…

% computing the fourth order approximations for the second order derivative % f''(x) = a*f(x-2*dx)+b*f(x-dx)+c*f(x)+d*f(x+dx)+e*f(x+2*dx)/dx^2 % f(x) = exp(x)*cos(x) % analytical_derivative f'(x) = exp(x)*[cos(x) - sin(x)] % f''(x) = - 2*exp(x)*sin(x) x=pi/3; analytical_derivative = - 2*exp(x)*sin(x) %computing the second…