Understanding Linear Systems

In this project, the second order derivative of a function is evaluated by numerical approximation method and then compared with the exact derivative. Taylor's table method is used to derive the expression for the second order derivative of a function, for a required order of accuracy and required scheme. (Central difference…

Objectives: Create the CAD model of Ahmed body and set up a coarse CFD simulation for flow around the Ahmed body. Calculate the Drag and Lift force/Downforce experienced by the body. Plot Velocity profile at different line probes and the experimental data with simulation data. Plot Velocity and Pressure distribution contours…

Objectives: Simulate a flow over NACA 2412 Airfoil. Calculate the Drag and Lift coefficient of the Airfoil. Simulate the flow for the various angle of attacks and compare the results. Simulate the flow using various Turbulence models and compare the results. Plot the velocity and pressure plots. Airfoil: An airfoil…

Objectives: Setup a transient Shock tube simulation. Plot the pressure and temperature plots in the domain. Plot the cell count as a function of time. Introduction: Shock tubes are the devices which are mostly used to study chemical kinetics. It basically is a tube with two chambers and a diaphragm separating the chambers.…

Objectives: Simulate flow of air through a solid pipe and study the heat transfer from the walls of the pipe to the fluid flowing inside the pipe. Run a grid dependence test to see the effect of changing grid size on the heat transfer. Study the effect of Supercycle stage interval and compare the simulation time in each…

(1) Need for Interpolation Schemes: In the FVM method, we need to evaluate the surface and volume integrals for the finite volume formulation. But sometimes the integrals have unknown variables whose value we need to determine at points other than the computational nodes. For such calculations, Interpolation schemes…

Objectives: Simulate a supersonic flow through a duct having a sharp corner to observe the formation of Shock waves. Literature review on Shock waves. Literature review on Shock wave boundary conditions. Observe the effect of SGS parameter on shock wave location. Observe the effect of SGS temperature value on cell count.…

Objectives of the Project: (1) Perform a transient simulation for the flow of air over a throttle body in Converge Studio and post-process the results in ParaView. (2) Show the plots for pressure, velocity, and mass flow rate. (3) The throttle valve should rotate by a given angle during the simulation time.   Geometry:…

Objectives of the Project: (1) Calculation of Flow Variables. (2) Generation of blockMeshDict using the wedge boundary condition. Create the blockMeshDict file in MATLAB such that the mesh is automatically created for various wedge angle. (3) Simulating the pipe flow in OpenFOAM using icoFoam solver. (4) Post process the…

Objectives of the Project: (1) Calculation of Flow Variables. (2) Generation of blockMeshDict using the wedge boundary condition. Create the blockMeshDict file in MATLAB such that the mesh is automatically created for various wedge angle. (3) Simulating the pipe flow in OpenFOAM using icoFoam solver. (4) Post process the…

Objectives of the Project: (1) Perform a steady state simulation for the flow of air over a throttle body in Converge Studio and post-process the results in ParaView. (2) Show the plots for pressure, velocity, and mass flow rate.   Geometry: The throttle inside the pipe is aligned parallel to the plane of the pipe.…

The 1D Linear convection equation is given as: The first step to solve the problem is to discretize the equation. The time derivative is discretized using a first-order approximation forward difference scheme, whereas a first-order approximation backward difference scheme is used to discretize the space derivative.   …

The 1D Linear convection equation is given as: The first step to solve the problem is to discretize the equation. The time derivative is discretized using a first-order approximation forward difference scheme, whereas a first-order approximation backward difference scheme is used to discretize the space derivative.  …

Project Objectives: (1) To simulate air flow through a Backward-facing step using CONVERGE Studio and Post-process using ParaView. (2) To conduct a grid independent test and study the Pressure and Velocity contour.   Geometry: length along x-axis = 0.27 m length along y-axis = 0.02 m length along z-axis = 0.025 m…

Project Objectives: (1) To simulate the air flow through a channel using CONVERGE Studio and post-process using ParaView. (2) To conduct a grid independent test and study the Velocity and Pressure contour.   Mesh sizes: X-direction -  2e-4 m 1.5e-4 m 1e-4 m Mesh along Y and Z direction is kept the same for all…

Genetic algorithm is an optimization technique which is used to determine the best value of an objective function from the given range of input variables. It is used to find the global maxima or minima of the function. In Matlab, we get the minimized value of function by default. The 'ga' function is coded in such way.…

clc clear all close all l1=1; l2=0.5; theta1=linspace(0,90,10); theta2=linspace(0,90,10); frame=1; for i=1:length(theta1) THETA1=theta1(i); for j=1:length(theta2) THETA2=theta2(j); x0=0; y0=0; x1=l1*cosd(THETA1); y1=l1*sind(THETA1); x2=x1+l2*cosd(THETA2); y2=y1+l2*sind(THETA2); plot([x0 x1],[y0 y1],[x1 x2],[y1 y2],'linewidth',3)…

clear all close all clc b=0.5; g=9.81; l=1; m=1; %initial conditions theta_0=[0;3]; %time points t_span=linspace(0,20,100); [t,theta]= ode45('ode_func1', t_span, theta_0); figure(1) plot(t,theta(:,1)) hold on plot(t,theta(:,2),'red') legend('displacement vs time','velocity vs time') figure(2) frame=1; for i=1:length(t_span)…

clc clear all close all gamma=1.4; t3=2300; t1=500; p1=101325; bore=0.1; stroke=0.1; cr=12; con_rod=0.15; v_swept=(pi/4)*bore^2*stroke; v_clearance=v_swept/(cr-1); v1=v_swept+v_clearance; v2=v_clearance; p2=p1*cr^gamma; t2=p2*v2*t1/(p1*v1); constant=p1*v1^gamma; V_12=engine_kinematics(bore,stroke,con_rod,cr,0,180); P_12=constant./V_12.^gamma;…

for linear polynomial clear all close all clc cp_data=load('data'); temperature=cp_data(:,1); cp=cp_data(:,2); [p,S,mu]=polyfit(temperature,cp,2); predicted_cp=polyval(p,temperature,S,mu); ste=sqrt(diag(inv(S.R)*inv(S.R')).*S.normr.^2./S.df); %to get uncertainity or standard deviation of coefficients plot(temperature,cp,'linewidth',2)…

A 3D model of Internal Geneva mechanism was made as per the dimensions given in the image and assembly was done in a manner so as to achieve the required motion of the mechanism. 3D Model: Motion Analysis was performed on the mechanism to calculate the contact forces between the slot in driven wheel and the driving wheel.…

1) Grid Dependence Test: 3 various configurations were used for creating mesh along x,y and z direction. Aim was to select the best mesh from those. Flowbench geometry was created in Solidworks. For this test, valve lift of 3 mm was kept constant for all the simulatons. A steady state simulation was done as we are looking…

Objectives of the Project: (1) Create the geometry using BlockMesh in OpenFOAM. (2) Simulate the flow using the icoFoam solver. (3) Compare the velocity magnitude profile for different values of mesh grading factor at a distance of 0.085m from the inlet. Theory: For this project, the lid-driven cavity tutorial provided…

Objectives of the Project: (1) Solve the Conservative and Non-conservative form of governing equation of Quasi 1-D Supersonic nozzle flow using the Maccormack method. (2) Compare the results of the Conservative and Non-conservative form. (3) Perform Grid dependence test.   Theory: The Maccormack method- This…

Objectives of the Project: (1) To determine the Eigenvalues of a given matrix. (2) To find the Iteration matrix and the spectral radius of the iteration matrix of Jacobi, Gauss-Seidel and SOR solvers. (3) Change the diagonal elements of the given matrix by a suitable constant and observe the change in spectral radius.…

This project computes the first order numerical derivative of a function according to the 1st order, 2nd order and 4th order approximation methods. This numerical derivative is compared with the exact derivative of the function and magnitude of error is obtained. The first order derivative of function according to first…

This project computes the first order numerical derivative of a function according to the 1st order, 2nd order and 4th order approximation methods. This numerical derivative is compared with the exact derivative of the function and magnitude of error is obtained. The first order derivative of function according to first…

Objectives of the project: 1) Obtain temperature distribution for a thin square plate by solving 2D conduction equation. 2) Solve for both- steady state as well as the transient state of the 2D heat conduction equation and compare the results. 3) Solve the transient state equation by explicit and implicit methods. 4) The…

Objectives of the Project: (1) Solve the 2D Conduction equation is Steady state as well as the Transient state. (2) Compare the time for Steady state simulation and Transient state simulation. Theory: In the 1st part of the project, the code for solving the 2D conduction equation is given for both steady state as well…

Objectives of the project: (1) State the reason for an unstable solution to 2D Transient state Conduction equation. (2) Effect of time-step on the stability of the solution. Theory: In the transient equation of 2D conduction equation, the presence of a time derivative term can give rise to an unstable solution…

A 3D model of Centrifugal pump is created in Solidworks. The following image shows the cut section of centrifugal pump. An open type of impeller of the pump is designed as shown. For the Flow simulation, moving reference method is used. In this method, the region around the fans of impeller is given a rotational velocity.…

In the given problem, pipe of outer diameter 100 mm and thickness 5 mm was considered. Simulation is carried out for flow of air through the pipe. 3 cases were analysed where Reynold's number has been varied in each case. 1) Re=100, Velocity=0.0164 m/s Velocity profile Velocity at 85%, 90% and 95% of length As seen from…

The main objective of this project is to study the effect of change in angle of attack on the lift and drag forces of the aerofoil. The simulation was performed considering the medium as air and the velocity as 600 m/s. It is a time dependent simulation with a timestep of 1 sec and effect of gravity is considered. Following…

Reynold's Number for a flow over a cylinder can be calculated using the given formula. Re = rho*U*D/mu D = cylinder diameter mu = dynamic viscosity rho = density   For this simulation, air is considered as the fluid. The properties of air are as follows: mu= 1.81*10^5 kg/(m.s) rho=1.225 kg/m^3 Also, D= 0.05 m  …

To solve this problem, I have taken three bodies with drag coefficient as 0.8, 0.5 and 0.2 respectively. The velocity with which body moves will be given by the user between 0 to 50 m/s.  The output graphs are obtained for the following: 1)  Drag force vs Drag coefficient for velocity given by user. 2) Drag force…

1. A=[1,2,3,4,5] This will generate a row vector. The output will be- [1 2 3 4 5]   2. B=[1;2;3;4;5] This will generate a column vector, such that the entry after semi-colon will be entered in a new row. The output of this statement will be- 1 2 3 4 5   3. C = A*B' This will multiply matrix A with the transpose…

Rankine cycle consists of 4 stages: Process 1-2: Isentropic compression in pump Process 2-3: Constant pressure Heat addition in Boiler Process 3-4: Isentropic expansion in Turbine Process 4-1: Constant pressure Heat rejection in Condenser At inlet of the steam turbine, steam is either in superheated state or in saturated…

1) Main file: Temperature array is defined at the start. Header is read in this file by using 'fgetl' command. The global high,medium and low temperatures are stored which will be used later. This file is where all other functions are called. clear all close all clc Temperature=linspace(300,5000,1000); %Header of the file…