Curve Fitting-Comparison of linear and cubic model

This is about the project I did during my Bachelors , i represented my team as Lead Designer in SAE ECOKART 2015. I made the space frame using engineering mechanics trusses concepts and did the FEA on it. I used the Impact analysis standard suggested by SAE India Team to find resuts of Impact analysis. I received Rs10,000…

(1) From the cantera results it\'s quite obvious that AFT is increasing linearly with increasing air temperature.Also when air temperature is high combustion will take place much before due to less ignition delays(chemical delay what i mean) and utilizing some energy by using heat exchanger will help in early combustion…

Obviously Conservative form of PDE is faster than non-conservative form of PDE. From the code following run time is noted: Solution time for conservative form is 2.28 secondsSolution time for non - conservative form is 5.39 seconds   Obtained graph is at 101 grid points(value of n in the code): It clearly indicates…

Python program is written to see the effect of equivalence ratio on AFT. The python program was written to calculate AFT using Newton-Raphson method of optimization: plot i got from the python code without cantera: with cantera module:   It indicates that cantera curve got much more curvy and its value(magnitude)…

This is the project I did during my intern at Tata Marcopolo Motors pvt ltd,Lucknow as a part of my academics in B.Tech. One of the semi low floor Bus Model was dealing with problem of failure of rear destination board bracket and I was given the job to find the reason behind that. This project epitomise a report on-…

Hagen Poisuelle\'s Equation, Del(p)=(32*mu*V*L/D2) L=1m D=20mm Kinematic Viscosity = 1.004008e-06 m^2/s,vel=5.02*10-2 m/s after putting these values, pressure drop comes out to be 4.024064e+00 pa. Now simulation has been run for both the symmetry n wedge conditions: Wedge Angle Maximum Velocity Percentage Error in Velocity…

Matlab Code for block mesh : clear all close all clc %input theta=2; %In degrees for Wedge angle grading=0.25; %Grading factor along the walls of cylinder length=1000; radius=10; b1=400; %cells along the length of cylinder b2=12; %cells along the radius of cylinder %vertices of the wedge v0=[0 0 0]; v1=[length 0 0]; v2=[length…

    Some of the interpolation schemes used are Linear, quadratic ,etc interpolation schemes. These methods are used toget to more realistic results as the engineering problems basically uses the real world environment.Here in FVM the use of volume instead of  a point makes that close to real problems and…

Here are the courant numbers obtained after doing with grading 0.2,0.5,0.8. 0.0899,0.3204 and 0.4981 respectively Plots obtained ffrom the three grading meshes are almost similar so theres not much change with that. Kinematic viscocity to be taken as 1e-5 Conclusion is that the accuracy is better in 0.2 graded mesh when…

Eigen Values of A comes out to be(for the A matrix given above and from code made in matlab): 6.1763 - 0.0000i -7.6663 - 0.0000i 8.4900 + 0.0000i function [eigVal]=eigen_value(A) s = size(A); I = eye(length(A)); % syms x eq1 = det(A-I*x) == 0 ; eigVal = double(solve(eq1,x)); % end On solving System using three methods…

Eigen Values of A comes out to be(for the A matrix given above and from code made in matlab): 6.1763 - 0.0000i -7.6663 - 0.0000i 8.4900 + 0.0000i function [eigVal]=eigen_value(A) s = size(A); I = eye(length(A)); % syms x eq1 = det(A-I*x) == 0 ; eigVal = double(solve(eq1,x)); % end On solving System using three methods…

Here plots at different dt is shown for both implicit and explicit methods reducing the dt value from 1 to 0.001. At around 0.45 CFL number the solution starts becoming unstable. close all clear all clc nx=10;ny=nx;dt=0.01;nt=2000;s=1e-4; x=linspace(0,1,nx);y=linspace(0,1,ny); z=fliplr(y);dx=(x(2)-x(1));dy=dx;f=(s*dt)/(dx^2);…

SOR seems to be the fastest iterative method for steady state and while for unsteady the fastest method seems to be implicit type as the time step here work as the loop structure for the same. SOR comes with least iterations among the three as its clear from the previous problem also.

Here from all the contour plots its shown that SOR gets the least iterations to converge the result with the required tolerance. close all clear all clc nx=12;ny=nx;er=1e-4;error=9e9;c=1; x=linspace(0,1,nx);y=linspace(0,1,ny); z=fliplr(y);f=1.5; t=ones([nx,ny]); t(1,2:nx)=600; t(1:ny-1,1)=400; t(2:ny,nx)=800; t(ny,1:nx)=900;…

Basically less the step size more is the simulation time as calculation gets higher. Solution is quite unstable for 1e-1 as there are lot of disturbances and, its best for 1e-2 as it seems close to stable, while its quite similar in case for 1e-3 and 1e-4. now the code i used is, clc clear all close all figure(1) tic hold…

On increasing the value of n,initially the curve gets better with its increase from n= 20 to n=80. But on n=160 we can see that disturbing waves starts falling on the result which is completely ruining it so its not stable at n=160. while at n=80 its the most stable and least stable is at n=20. %Inputs for the linear convection…

1. Kinematic viscosity : It is the ratio of dynamatic viscosity to the density of the fluid; ν = μ/ρ. The SI unit is :m^2/sec. 2. Dynamic viscosity : It is the ratio of shearing stress to shear rate of the parallel layers in the fluid; μ = Τ/Υ. The SI unit is (N*sec)/m^2. 3.…

From the graph, its seen that the FDS and BDS methods give a higher error compared with the skewed methods.In a skewed scheme, its taken into account more than one data points for calculating the data at any particular point.This helps us to get more accurate values.Sometimes when evaluating a point the left side function…

Plot shows that error in fourth order is quite less as compared to the second and first order. My Legends were not coming due to some software bugs,I will try to fix it by downloading it clc close all clear all dx=pi/40:pi/1000:pi/20 for i=1:length(dx) error1(i)=errorfds(dx(i)); error2(i)=errorcds(dx(i)); error3(i)=errorfourth(dx(i));…

%Numerical derivative vs exact derivative clear all close all clc %function=sin(x)/x^3; x=pi/3; %analytical derivative=(x^3*cos(x)-sin(x)*3*x^2)/x^6; analytical_derivative=(x^3*cos(x)-sin(x)*3*x^2)/x^6; %numerical derivative dx=pi/25; %spacing between the grid points %1.first order approximation %forward differencing scheme…

clc close all clear all dx=pi/40:pi/1000:pi/20 for i=1:length(dx) error1(i)=errorfds(dx(i)); error2(i)=errorcds(dx(i)); error3(i)=errorfourth(dx(i)); end hold on plot(dx,error1,\'r\') % red line is the first order derivative plot(dx,error2,\'y\') % yellow line is the second order derivative plot(dx,error3,\'b\') % blue…

ar of alkane = (3*n+1)/2ar of alkene = (3*n)/2ar of alkyne = (3*n-1)/2   %Stoichiometric Combustion Calculator for Alkane, Alkene and Alkyne fuels %ar = stochiometric coefficient %n = number of moles of C % alkane = CnH2n+2. % alkene = CnH2n. % alkyne = CnH2n-2 % There ar for above compounds be as follows n=1:1:20;…

Video @ https://youtu.be/zVI0960uRGw   (1) function [dtheta_dt]= ode_func(t,theta,w) theta1=theta(1) theta2=theta(2) dtheta1_dt=theta2; dtheta2_dt=-(w*w)*sin(theta1); dtheta_dt=[dtheta1_dt;dtheta2_dt]; end (2) %sp clear all close all clc g=9.81; l=1; m=0.1; w=g/(l*m); theta_a=[0;1]; t_span = linspace(0,1,500); [t,results]=ode45(@(t,theta)…

1. DIVERGENCE Divergence is the dot product of nabla operator with a vector field.The word DIVERGENCE itself provides a physical insight that, it means the how well those immediate vectors surrounding the point move away from that point. Thus positive divergence means vectors moving away from the point of interest, and…

Boundary conditions are those which depends on space while initial conditions are depends on time. So, in boundary condition space coordinate will be varied and in initial conditions time will be varied. while dealing with boundary conditions we can have multiple solutions while initial conditions problem gives unique…

1.A=[1,2,3,4,5] denotes a coloumn vector 2.B=[1;2;3;4;5] denotes a row vector 3.C=A*B\' means A* TRANSPOSE OF B BUT ITS NOT POSSIBLE AS AS Matrix dimension is invalid for multiplication 4.C=B*A means MULTIPLICATION OF B INTO A gives   1 2 3 4    5       as the resultant matrix. …

https://projects.skill-lync.com/projects/pipe-flow-simulation-47303 velocity is seen to be higher at 0.85 of length than 0.90 theh 0.95 of length.

for reynolds number at 100 - assuming to be laminar flow for reynolds number at 1000 - assuming to be laminar and turbulent for reynolds number at 10000 - assuming to be only turbulent

1.(1)popt stores the best coefficients of the function from the samples. 1.(2)pcov gives the variance and covariance which is returned from the curve_fit 2.np.array(temperature) passes the whole array of temperature samples to the function. 3.If we got more than one coefficients in popt to send then *popt is used to send…

https://projects.skill-lync.com/projects/Otto-CYCLE-PV-PLOTS-AND-THERMAL-EFFICIENCY-60372 import math import matplotlib.pyplot as plt #inputs p1=101325 t1=500 gamma=1.4 t3=2300 #geometric parameters bore=0.1 stroke=0.1 con_rod=0.15 cr=12 #volume computation v_s= (math.pi/4)*pow(bore,2)*stroke; v_c= v_s/(cr-1); v1=v_s+v_c;…

import math import matplotlib.pyplot as plt #inputs p1=101325 t1=500 gamma=1.4 t3=2300 #geometric parameters bore=0.1 stroke=0.1 con_rod=0.15 cr=12 #volume computation v_s= (math.pi/4)*pow(bore,2)*stroke; v_c= v_s/(cr-1); v1=v_s+v_c; def engine_kinematic(start_crank,end_crank) : a=stroke/2 R=con_rod/a sc=math.radians(start_crank)…

cp_data=load(\'data\');temperature=cp_data(:,1);cp=cp_data(:,2); % original data plotplot(temperature,cp); coeff_lin=polyfit(temperature,cp,1);coeff_cubic=polyfit(temperature,cp,3);predicted_lin=polyval(coeff_lin,temperature);predicted_cubic=polyval(coeff_cubic,temperature); hold on;plot(temperature,predicted_lin);plot(temperature,predicted_cubic);xlabel(\'Temperature[K]\');ylabel(\'Sp.…

import matplotlib.pyplot as plt#Velocity(m/s^2)v = 10 #Density(kg/m^3)rho = 1.2 #Areas(m^2)areas = [0.5,0.25,2,1.45,2.8] #Drag Coefficientsc_d = 0.8 #Drag Forcedrag_force = [] for area in areas:   drag_force.append(0.5*rho*area*c_d*v*v) plt.figure(1)plt.plot(areas,drag_force)plt.title(\"Area vs Drag Force\")plt.xlabel(\"Area\")plt.ylabel(\"Drag…

% part 1 %coefficient of dragcd=0.6;%velocity vectorvel=1:100;%densityden=1.2;%frontal areafa=1.5;%drag forcedf=0.5*cd*den*fa*vel.^2;%plot drag force vs velocityplot(vel,df)xlabel(\'VELOCITY->\')ylabel(\'DRAG FORCE->\')   %part 2 %frontal area of different shapesfa_square=1*1;fa_rectangle=1*1.2;fa_circle=pi*1^2/4;fa_triangle=0.5*1*1;fa=[fa_square,fa_rectangle,fa_circle,fa_triangle];%density,vel,coefficient…

%row_vector row=[1,2,3,4,5]; %coloumn vector col=[1;2;3;4;5];

\"\"\" Part 1:Drag force vs velocity function \"\"\" import matplotlib.pyplot as pltdef plot(cd,density,vel,area): drag_forces=[] for velocity in vel: drag_forces.append((0.5*density**area*cd*velocity*velocity)) plt.plot(vel,drag_forces ) plt.xlabel(\'Velocity\') plt.ylabel(\'Drag force\') plt.show() return; plot(0.8,1.2,[5,6,7,8,9,10,11,12],0.1)…

% RANKINE SIMULATORprompt=\' RANKINE SIMULATOR\\n\\n1-2 is Isentropic Expansion in the turbine.\\n2-3 is Constant Pressure Heat Rejection by condensor\\n3-4 is Isentropic Compression in the pump\\n4-1 Constant Pressure Heat Addition by boiler\\nEnter the pressure at inlet of turbine(MPa):\';p1=input(prompt);prompt=\'Enter…

%Part 1 To extract 14 coeff function [coeff]= search_element(x) f=fopen(\'therm.dat\',\'r\'); x1=[x,\' \'];for i=1:200 g1=fgetl(f); if strfind(g1,x1) break; endendg1=fgetl(f);g2=fgetl(f);g3=fgetl(f);coeff=data_extractions(g1,g2,g3);end   function [coeff]=data_extractions(a1,a2,a3) j=findstr(a1,\'E\');k=findstr(a2,\'E\');m=findstr(a3,\'E\');…

Genetic algorithm is a kind of artificial Intelligence that optimizes the function by doing the cross overs n mutations like in normal reproduction process(Survival of the fittest).Optimization stops when it got reached to the fitness value or the time limit. clear allclose allclcx=linspace(0,0.6,150)y=linspace(0,0.6,150)[xx…

Video @ https://youtu.be/zVI0960uRGw   (1) function [dtheta_dt]= ode_func(t,theta,w) theta1=theta(1) theta2=theta(2) dtheta1_dt=theta2; dtheta2_dt=-(w*w)*sin(theta1); dtheta_dt=[dtheta1_dt;dtheta2_dt]; end (2) %sp clear all close all clc g=9.81; l=1; m=0.1; w=g/(l*m); theta_a=[0;1]; t_span = linspace(0,1,500); [t,results]=ode45(@(t,theta)…

THERMAl efficiency= 0.6299 %code% %function% function [v] = engine_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank) a=stroke/2R=con_rod/a v_s=pi/4*bore^2*stroke;v_c=v_s/(cr-1); theta = linspace(start_crank,end_crank,100); term1=0.5*(cr-1);term2=R+1 -cosd(theta);term3=(R^2-sind(theta).^2).^0.5; v=(1+ term1*(term2…

% part 1 %coefficient of dragcd=0.6;%velocity vectorvel=1:100;%densityden=1.2;%frontal areafa=1.5;%drag forcedf=0.5*cd*den*fa*vel.^2;%plot drag force vs velocityplot(vel,df)xlabel(\'VELOCITY->\')ylabel(\'DRAG FORCE->\')   %part 2 %frontal area of different shapesfa_square=1*1;fa_rectangle=1*1.2;fa_circle=pi*1^2/4;fa_triangle=0.5*1*1;fa=[fa_square,fa_rectangle,fa_circle,fa_triangle];%density,vel,coefficient…