Solving linear equation using Iterative methods and analysis of the spectral radius of the Matrix.

Steady state stimulation over a throttle body with fixed embedding  The valve is completely open, the mesh 2e-3 m in X,Y and Z respectively. fixed embedding is used with a embedding of a factor of 3 for 2 layers. for boundary condition the inlet pressure is 1.5 bar and the outlet pressure is of 1 bar the pressure…

gri30_mix is used to compute mixture properties it contains diffusion co-efficient etc.   Introduction:  In this study, we will be looking at the 1-D reactors basically to calculate flame speed. There are different types of 1-D reactors such as freely propagating flame, burner stabilized flame, etc. Our primary…

Objective: To write a code that takes all the reactions from the GRI mechanism and calculates 10 most sensitive reactions. Sensitivity parameter is Temperature. ------------------------------------------------------------------------------------------------------------------------------ What is Sensitivity Analysis - Sensitivity…

Laminar Pipe Flow Simulation in OpenFOAM Part-1 [Wedge Boundary condition]: Objectives: 1) Calculating the pre-elementary properties related to the flow according to the Hagen-Poiseuille equation. 2) Creating the mesh script(blockMeshdict file) for specifying the geometry and boundary condition. 3) Creating a MATLAB program…

Laminar pipe flow simulation in OpenFOAM Part -II [ Symmetry boundary condition ] Objectives: 1. Creating the block mesh dict file in OpenFOAM using the symmetry boundary condition  2. Simulation result for angles 10, 25, and 45 and post-processing the velocity profiles. 3. Comparison between the results of symmetry…

Objective: To run three different cases of mixing - t problem to compare mixing efficiency following are the three cases - 1) Short mixing tee with a hot inlet velocity of 3m/s and Momentum ratio of 2. 2) Long mixing tee with a hot inlet velocity of 3m/s and Momentum ratio of 2. 3) Short mixing with a hot inlet velocity…

Objective: Part - I To determine Auto-ignition delay for Methane combustion for the given two cases- a) For temperature varying from 950 K to 1450 K while keeping the pressure constant. b) For pressure varying from 1 atm - 5 atm while keeping the temperature constant. Part - II For the given two cases plotting the change…

Objectives of this study: Simulating 1-D wave equation in Matlab assuming the initial velocity profile as a step function. Studying the effect of grid-size on the solution of the 1-D wave equation. Studying the effect of the time step on the solution. -----------------------------------------------------------------------------------------------------------------------------…

Problem: Co-efficient Matrix- `A= [ [ 5,1,2 ],[-3,9,4],[1,2,-7] ]` The R.H.S- `b = [[10],[-14],[33]]` Solution Matrix- `X= [[x_1],[x_2],[x_3]]` The above system of linear equations are solved using the iterative methods which are: 1. Gauss- Jacobi  2. Gauss-Siedel 3. Successive over-relaxation(SOR) method After this,…

Objective: Solve the given system of coupled non-linear equation using Multivariate Newton Raphson method(using Implicit Euler Method/Backward Differencing). `dy_1/(dt) = -0.04y_1 + 10^4y_2y_3` `dy_2/(dt) = 0.04y_1 - 10^4y_2y_3-3*10^7y_2^2` `dy_3/(dt) = 3*10^7y_2^2` -----------------------------------------------------------------------------------------------------------------------------------…

Mesh Generation and Analysis using blockMesh for a FLow over a Backward-Facing Step. Objectives: To create the desired geometry using blockMesh. Specifying the boundary and initial conditions for this particular problem. Running the case for different grading factors and comparing the results for the velocity at x = 0.085…

Internal Combustion Engine Simulation. A transient Simulating of an IC engine using Converge Studio was performed. Following are the various engine parameters: Engine Geometric Parameters Bore =0.086 m Stroke = 0.09 m Connecting rod length = 0.18 m RPM = 3000 Simulation time parameters Start time: -520 degree  end…

Objective: 1. Calculate Adiabatic Flame temperature for Methane Combustion(constant volume chamber) for different equivalence ratio by writing a programme in python. 2. Perform the same calculations as stated above by using Cantera and comparing the results. 3. Calculate the AFT for the constant pressure chamber with heat…

Objective: To run simulations for two types of pistons and characterize the emissions for Diesel Engine (Soot, Nox, and UHC) Two pistons for this objective are Open-W type piston and Omega Piston. #Creating a sector geometry using make surface: For this diesel engine simulation, a closed cycle analysis is done i.e. when…

Flow over backward facing step  Ran the case for three different mesh sizes and post processed the result, following are the three different mesh sizes for which the case was ran. 1- 2e-4m 2- 1.9e-4m 3- 1.8e-4m velocity in x and y direction is compared in the post process the main flow takes place in the x direction…

 Below are the velocity Graphs in paraview (in x and y coordinate not in z as in z direction the velocity is zero) for different mesh sizes  1- 2e-4m 2- 1.5e-4m 3- 1e-4m https://drive.google.com/drive/folders/1EKIFX-AHctoVc9vwXxUuGP66KBzU3mnP

Different objectives of this study. 1. The 2D heat equation is solved using iterative solvers       a. Solving Un-Steady 2-D heat equation for both explicit and implicit forms of the equation using iterative methods such as:           i. Gauss Jacobi        …

3. ANALYSIS OF NUMERICAL STABILITY OF THE SOLUTION FOR TRANSIENT 2D HEAT CONDUCTION: A scheme is said to be stable if the errors (truncation, round-off etc) decay as the computation proceeds from one marching step to the next. A scheme is stable if the errors made at a one-time step of the calculation do not cause the…

Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method Objectives: Simulation of 1D Super-sonic nozzle flow using the governing equation in both Conservative and Non-Conservative form. Demonstrating time-wise variation of density, temperature, velocity and Mach number at the throat. Demonstrating…

Objective: To derive a fourth order scheme for a second order derivative using Central, Skewed right and Skewed left schemes.  For deriving the fourth order approximation of second order derivative Taylor table method is used. Determining the number of terms for the scheme: for skewed scheme = p+q for central scheme…

Boundry Condition:There are mainly two types of boundary conditions Dirichlet and Neumann boundary conditions and sometimes they are used together(mixed boundary condition). When using a Dirichlet boundary condition, the value  of the vaiable is prescribed at the bounary. Whereas, when a Neumann Boundry condition…

The governing equations for the boundary layers are the Navier Stokes equation shown below: `(du)/dx + (dv)/dy = 0` - continuity equation` `rho((du)/dt + u(du)/dx + v(du)/dy)= -(dp)/dx + mu(d^2u)/dy^2` - Momentum Equation` `62rhoc((dT)/dt+ u(dT)/dx+v(dT)/dy)=K(d^2T)/dx^2+mu((du)/dy)^2` - Energy equation. Applying Reynold\'s…

Shock Tube Simulation: A shock tube simulation case is setup with a high pressure region containing Nitrogen and a low pressure region containing oxygen. Shock Tube: The shock tube is a device in which a plane propagating shock is produced in a long tube bythe abrupt rupturing of the diaphragm separating one section of…

Conjugate Heat Transfer: Setteing up the case setup for the conjugate heat transfer problem in a pipe(made of aluminium) with fluid flow inside and a added heat flux into the domain through soild. The case is setup to predict the heat transfer in the fluid and soild regions respectively. What is Supercycling: The case…