Week 3 - Solving second order ODEs

OBJECTIVE : Write a python code to find out the minimum value of pressure at h=0.6ft by using the Newton Raphson method. Write a python code to find the optimal relaxation factor for this problem with the help of a suitable plot. Write a python code to tabulate the results of pressure for h = [0.6,1.2,1.8,2.4,3,3.6,4.2]…

AIM : To write a python script to analyze the data available in the given file. OBJECTIVE : Check the compatibility of the file Calculate the area under the P-V diagram.  Calculate the power output of this engine assuming that RPM is 1500 Calculate its specific fuel consumption. THEORY : Parsing means to break it…

AIM : To write a code in Python to fit a linear and cubic order polynomial for the given Cp data. THEORY : Curve fitting is the process of constructing a curve or mathematical function that has the best fit to a series of data points, possibly subject to constraints or it can be defined as the process of finding…

AIM:  To write a python program that represents the(ODE) equation of motion of a simple pendulum with damping. THEORY:  The second-order ODE is simple pendulum's harmonic motion with damper, hence with decreasing amplitude. `(d^2theta)/(dt^2)+(b/m)*((d theta)/(dt))+(g/L)*sin(theta)=0` This system is equivalent…

OBJECTIVE: To create the PV diagram of Otto Cycle for the given inputs such as engine dimensions, pressure, and temperature, using Python programming. To obtain the thermal efficiency of the engine. CODE:   #otto cycle simulator import math import matplotlib.pyplot as plt def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank):…

AIM :   To design a 3D model of centrifugal pump ,run a baseline flow simulation where inlet flow takes place and then perform a parametric study for different velocities and then to obtain the relationship between Pressure ratio and mass flow rate. 3D Model Parameters: Internal flow simulationSteady-state studyTemperature:…

AIM: To perform the flow simulation through a flow bench by modeling the geometry and obtaining a lift vs mass flow rate plot.  Grid dependence test For three grids run the simulation at a particular valve lift and explain the result. Effect of valve lift on mass flow rate After deciding the best grid, run a parametric…

AIM: To model the flow over NACA0017 airfoil and compare the lift and drag force for the angle of attack 0,2,4,6,8,10.  THEORY: Airfoil is defined as the cross-section of a body(shape of wing, blade of propeller rotor or turbine or sail) that is placed in an airstream in order to generate useful aerodynamic force.…

AIM: To simulate flow over a cylinder at different Reynold's number conditions. Increase Reynold's number by a factor of 20%, 40%, and 100% then run the transient simulation. Create animations for pressure-velocity for all the three Reynolds number. THEORY: The Reynolds number (Re) is an important dimensionless…

AIM :   Simulation of isentropic flow through a quasi 1D subsonic-supersonic nozzle using  MacCormack's technique and to determine the steady-state temperature distribution for the flow-field variables and investigate the difference between the two forms of governing equations(conservative and non-conservative…

AIM : To write a MATLAB code for symmetry boundary conditions of laminar flow through pipe and to obtain the results at 10,25,45 degrees angles of pipe flow.Also to compare it with the results previously obtained for wedge boundary conditions. THEORY :  Since this is a continuation of a previous challenge (laminar…

AIM : To simulate the laminar flow of water through a circular pipe with the icoFoam solver and compare the results of simulation with the analytical solutions given by Hagen Poiseuille equations and to write a Matlab program that can generate the computational mesh automatically for any wedge angle and grading schemes.…

AIM : To simulate the flow through a backward facing step using the icoFoam solver in OpenFOAM software and to study the effect of mesh grading factor on the velocity and pressure magnitude profile. THEORY : Mesh Specifications: Number of cells along the x direction (longer dimension) = 200 Number of cells along the longer y…

AIM :  To write the code which solves the steady and unsteady 2D heat conduction equation by using the point iterative techniques by implementing the following methods. Jacobi  Gauss-Seidel Successive over-relaxation THEORY : Considering general 3D heat condution equation which has both time derivative and…

AIM : To write a program in Matlab to evaluate the second-order derivative of the analytical function exp(x)*cos(x) and compare it with the 3 numerical approximations that you have derived. DESCRIPTION : Taylor Table is a type of table which contains the data of all the Taylor series expansion of a function that…

AIM: To create a Rankine Cycle Simulator using MATLAB and to calculate the state points of Rankine Cycle based on user inputs, also to calculate the net work output and back work ratio and finally to plot the T-s and h-s diagrams . THEORY: The Rankine cycle is a model used to predict the performance of steam…

The above 3 pics are for O2, below 3 for CO2 The below one is for N2   AIM : File parsing the NASA thermodynamic data and to plot the variation of parameters like enthalpy,entropy,specific heat against temperature and to determine the molecular masses of individual species mentioned in the data file . THEORY…

AIM : To write a program that represents the(ODE) equation of motion of a simple pendulum with damping THEORY : The second order ODE is simple pendulum's harmonic motion with damper ,hence with decreasing amplitude. `(d^2theta)/(dt^2)+b/m(d theta)/dt+g/Lsin theta=0` This system is equivalent to mass attached…

AIM : To create and optimize stalagmite function  and to find the global maxima of function THEORY : Genetic algorithm is an optimization technique which is used to minimise a certain function,when used in optimization ,generally its purpose to minimise the error of a function.This algorithm is named 'Genetic, because…