Week 3 - Solving second order ODEs

Question: 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 = 800 K   Objectives: You will implement the following methods…

Question: In this challenge, you are going to simulate an incompressible-laminar-viscous flow through the backward facing step geometry. You should perform a transient simulation. The solver can be chosen based on the described physics of the flow. You need to explain the entire simulation procedure (how you set up the…

  Question: In this challenge you are going to simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle. You will derive both the conservation and non-conservation forms of the governing equations and solve them using the MacCormack's technique. You need to determine the steady-state temperature distribution…

Function Code: function [error_CD] = central_diffrencing(x,dx,x_CD) %anonymous function f=@(x) exp(x).*cos(x) %analytical derrivative analytical_derrivative = -2*exp(x)*sin(x) %central diffrencing central_diffrencing_approx = (x_CD(1).*f(x-2.*dx)+x_CD(2).*f(x-dx)+x_CD(3).*f(x)+x_CD(4).*f(x+dx)+x_CD(5).*f(x+2.*dx))./(dx.^2);…

Aim & Objective: For the given model, check and solve all geometrical errors and Assign appropriate PIDs. Perform meshing with the suitable Target length and element Quality criteria Target lengths for the different parts of a model can be decided by your own. Finer mesh will give good results and will compromise with…

Aim & Objectives: For the given models, check for the geometrical errors and delete surfaces which are unwanted for Surface wrap as shown in the videos. After clearing geometry, Merge all 3 models and perform surface wrap. Target length for Wrap = 3 mm Write a detailed report on steps followed to finish this challenge.…

Aim: For the given model, check and solve all geometrical errors on half portion and Assign appropriate PIDs. Perform meshing with the given Target length and element Quality criteria. After meshing the half model, Do symmetry to the other side. Objective: Target lengths for the different parts of a model are as follow:…

Aim: For the given model, check for the geometrical errors to make appropriate volumes. Create and assign PIDs as shown in the video. Perform surface mesh with the given target lengths as per PIDs Objective : For the given model, check for the geometrical errors to make appropriate volumes. Create and assign PIDs as shown…

Aim: For the given model, check for the geometrical errors and perform Topology cleanup accordingly. Set three different target lengths as three different cases and mesh the model. Objective : Target length = 1mm, 3 mm and 5 mm (i.e. 3 cases) Element type = Tria Apply any one target length from the above at a time for…

Aim:- To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop.   Objective:- To write a few words about any four empirical models used to calculate the cyclone separator efficiency.  To perform an analysis on a given cyclone separator model by varying the particle…

Aim: For this challenge, you will have to perform a parametric study on the gate valve simulation by setting the opening from 10 % to 80%. Objective: Obtain the mass flow rates at the outlet for each design point. Calculate the flow coefficient and flow factor for each opening and plot the graph. Discuss the results of…

AIM: Perform a steady-state conjugate heat transfer analysis on a model of a graphics card. You can use appropriate materials of your choice for the simulation. Make sure to properly define the correct solid and fluid zones. Refer the video for further clarification and the model is provided below the video. Run the simulation…

Objectives : Give a brief description of why and where a CHT analysis is used. Maintain the y+ value according to the turbulence model and justify the results.  Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas. How would you…

AIM : Run the simulation for the velocity of 25 m/sec with the default air properties in fluent. Questions : Q1. Describe Ahmed's body and its importance. Q2. Explain the reason for the negative pressure in the wake region.  Q3. Explain the significance of the point of separation.   Objectives : Velocity and pressure contours. …

Aim and Objective : What are some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves? In your own words, explain how these mathematical models have been adapted for CFD calculations. Perform the Rayleigh Taylor instability simulation for 2 different mesh sizes with the base…

Objectives : Give a brief description of why and where a CHT analysis is used. Maintain the y+ value according to the turbulence model and justify the results.  Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas. How would you…

AIM : Run the simulation for the velocity of 25 m/sec with the default air properties in fluent. Questions : Q1. Describe Ahmed's body and its importance. Q2. Explain the reason for the negative pressure in the wake region.  Q3. Explain the significance of the point of separation.   Objectives : Velocity and…

AIM: Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. Questions : PART-I Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.  PART-II Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000…

AIM: to set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 360C & the Cold inlet is at 190C. Use the k-epsilon and k-omega SST model for the first case and based on your judgment use the more suitable model for further cases. Giving the reason for choosing a suitable…

#python code for Data analysis #importing libraries import math import matplotlib.pyplot as plt import numpy as np from numpy import trapz #opening file file_name = 'engine_data.out' #compatibility check try: data = open(file_name,'r') print('\ndata file is open sucessfully.') except FileNotFoundError: print('\npls enter…

import math import matplotlib.pyplot as plt import numpy as np from scipy.optimize import curve_fit #linear curve fit function def func(t,a,b): return a*t + b #reading the data file def read_file(): temperature = [] cp = [] for line in open('data','r'): values = line.split(',') temperature.append(float(values[0])) cp.append(float(values[1]))…

# Libraries import math import numpy as np import matplotlib.pyplot as plt from scipy.integrate import odeint #defining Function def model(theta,t,b,g,l,m): theta1 = theta[0] theta2 = theta[1] dtheta1_dt = theta2 dtheta2_dt = -(b/m)*theta2 - (g/l)*math.sin(theta1) dtheta_dt = [dtheta1_dt,dtheta2_dt] return dtheta_dt #…

import math import matplotlib.pyplot as plt def engine_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank): #geometric parameters a = stroke/2 R = con_rod/a # volume parameters V_s = math.pi*(1/4)*pow(bore,2)*stroke V_c = V_s/(cr-1) sc = math.radians(start_crank) ec = math.radians(end_crank) num_values = 50 dtheta…

clear close clc %open the file f=fopen("THERMO.dat"); %using for loop for first 5 lines for i=1:5 %fgetl read line from each file fgetl(f) end for j=1:53 b=fgetl(f); %spliting the string based on delimiter a=strsplit(b,' '); % 1st cell of a represents the species_name species_name=a{1}; %extraction of local temperature…

function script function [f]=stalagmite(v) x=v(1); y=v(2); f1x=(sin((5.1*pi*x)+0.5))^6; f1y=(sin((5.1*pi*y)+0.5))^6; f2x=exp(-4*log(2)*(((x-0.0667)^2)/0.64)); f2y=exp(-4*log(2)*(((y-0.0667)^2)/0.64)); f=-(f1x*f1y*f2x*f2y); end Main script clear close clc %defining search space x=linspace(0,0.6,150); y=linspace(0,0.6,150);…

Function script  function [dtheta_dt] = ode_fun(t,theta,b,g,l,m) theta1 = theta(1) theta2 = theta(2) dtheta1_dt = theta2; dtheta2_dt = -(b/m)*theta2 - (g/l)*sind(theta1); dtheta_dt = [dtheta1_dt;dtheta2_dt]; end main script clear close clc %defining the inputs to variable b=0.05; g=9.81; l=0.75; m=1; %initial ciondition…

first of all we will plot simple non moving arms by fixed angle and co,ordinates for which we use following steps ; step 1- we gives the inputs like value of theta and length(l1 , l2) step 2-after giving inputs we wil calculate coordinates (x0,x1,x2) (y0,y1,y2) by using equation x1=l1cosd(theta1) , but we got the error(1.1)…