Objective to derive the `4^(th)`order approximation scheme of the second-order derivative. Central differencing Skewed right-sided difference Skewed left-sided difference To write a program in MATLAB to evaluate the second-order derivative of the analytical function, i.e., and compare with the 3 numerical approximations…

The heat equation is a second order partial differential equation that describes how the distribution of some quantity such as heat evolves over time in a solid medium, as it spontaneously flows from place where it is higher towards places where it is lower. It is a special case of the diffusion equation. For a function…

Objective: - To simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle using both the conservative and non- conservative Forms of the governing equations and solve them using the McCormack’s technique and comparing their solutions. Description: We consider the study, isentropic flow through a…

INTRODUCTION Studying the flow behaviour through various structures is an important subject for a CFD engineer.  When fluids flow through different geometries they exhibit different velocity, pressure and flow properties. in this project, simulation of a flow through backward facing step is done by studying the flow…

Objective: - To describe the need for interpolation scheme and flux limiters in FVM.   Basic In computational fluid dynamics there are 3 numerical methods-based solvers to solve the governing navier stokes equations. Finite difference method Finite volume method Finite element method Finite difference method The grid…

Objective: simulation of flow through pipe. To validate hydro-dynamic length with the numerical result. To validate the fully developed flow velocity profile with its analytical profile. To validate maximum velocity and pressure drop for fully developed flow. To post process shear stress and validate wall shear stress…

Objective: simulation of flow through pipe. To validate hydro-dynamic length with the numerical result. To validate the fully developed flow velocity profile with its analytical profile. To validate maximum velocity and pressure drop for fully developed flow. To post process shear stress and validate wall shear stress…

Objective: - To simulate the flow of hot and cold air through mixing tee and understand the effect of momentum ration and length on result.      Introduction Mixing is a unit process that involves manipulation of a heterogeneous physical system with the intent to make it more homogeneous. Mixing…

Aim: - To simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. Objective: - To setup case for steady and transient simulation. To calculate the coefficient of drag and lift over a cylinder by setting different Reynolds numbers. To observe the effect of Reynolds number on coefficient of…

Objective: To perform the grid independency test on Ahmed body. Expected result: Velocity and pressure contour. The drag coefficient plot for refined case. The vector plot showing the wake region. Provide drag and lift coefficient value for each case. Given data Flow velocity of air = 25 m/sec. The geometry of the Ahmed…

  Objective: observing the thermal behavior of hot fluid flowing through the exhaust pipe, and obtaining an accurate value of the heat transfer coefficient on the internal solid surface on the exhaust manifold. Introduction Conjugate heat transfer analysis is used to capture accurate heat transfer behavior due to…

Objective:  To perform Rayleigh Taylor instability simulation. Introduction Rayleigh Taylor instability is a phenomenon that occurs at the interface of fluids of different densities wherein the lighter fluid pushes the heavier fluid due to the density difference. it is a dynamic process wherein the system tries to…

Objective: To perform a steady state conjugate heat transfer analysis on a model of graphics card. introduction The term conjugate heat transfer (CHT) describes the process which involves variation of temperature within solids and fluids, due to thermal interaction between the solids and fluids, the exchange of thermal…

Objective: To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop. Introduction Cyclone separators are separation devices that use the principle of inertia to remove particulate matter from flue gases. Cyclone separator is one of many air pollution control devices known…

Objective: to perform a parametric study on the gate valve simulation by setting the opening from 10 to 80%. 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 result of the mass flow rate and flow coefficient.…

Aim: To perform a combustion simulation on the combustor model and plot the variation of the mass fraction of the different species in the simulation. Objective: Part 1 To perform a combustion simulation and plot the variation of mass fraction of different species in the simulation using line probe at different locations.…

Objective:  To study the effect of equivalence ratio on Adiabatic flame temperature for methane. To study the flame temperature variation with heat loss. To study the AFT variation with alkane, alkene, alkyne. To study the variation of AFT with no. of carbon atoms in chain. Adiabatic Flame Temperature The chemical…

 Objective:  To study the effect of preheating on Adiabatic Flame Temperature (AFT). To study the effect of preheating on Combustion efficiency (`eta`). Introduction A recuperator is a heat exchanger in which energy from a steady flow of hot combustion products, i.e., flue gases is transferred to the air supplied…

Objective: To create various mixture using Quantity class in Cantera. 1.  Use the "moles" method/function, calculate the number of moles of the object A and explain how it is calculated analytically. You need to use this after line number 9 by using the predefined function ‘A.moles’ Mixture used for…

Objective: To derive the reaction rate ODEs & production of each species for the simple reaction mechanism and represent it in the form of compact notations. and write desired matrices. `R_1 text( ) CO+O_2underset(k_(r_1))(overset(k_(f_1))↔)CO_2+O` `R_2 text( ) CO+OHunderset(k_(r_2))(overset(k_(f_2))↔)CO_2+H`…

When does an ODE become unstable? Increments of time and space appear throughout the differential equation. Stability is achieved for the explicit approach problem by limiting the value of time increment `(Deltat)` for a particular vaue of space increment `(Deltax)`. if the value of `Deltat` is larger than the limit imposed…

Objective: To solve the Set of equations given below 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*10^1y_2^2` Given data Initial guesses for y `y_1 = 1` `y_2=0` `y_3=0` `alpha=1` `time=10 text( minute)` Theory From the above set…

Objective To plot the variation of Auto-ignition time of methane with a constant Temperature of 1250 K and varying pressure of 1 to 5 atm. To plot the variation of Auto-ignition time of methane with a constant pressure of 5atm and varying temperature from 950 to 1450 K. To observe and print the rate of change of molar…

Aim: To determine the 10 most sensitive reactions with respect to temperature among the list of reactions in the GRI mechanism for combustion. Objective:  Plot the variation of temperature and molar concentration of the species with respect to time. Plot the bar graph showing the 10 most sensitive reactions with…

Objective: To check for the geometrical errors and perform topology cleanup. set three different target lengths (1,3 and 5mm) as three different cases and mesh the model. Procedure Import geometry Perform geometry checkup.select single cons to visualize on model.in the above figure white marked cons are single entities.single…

Objective To check geometrical errors to make appropriate volume. To create and assign PID's as shown in video. To perform surface meshing with given target length. Blade stage-1 =1mm Blade stage-2 =1mm Impeller = 2mm Shaft rotor = 1mm Turbo casing = 5mm Compressor casing = 5mm Inlet casing cover = 5mm To perform volumetric…

Aim: To clean up the given model of the BMW car so that no single coons are present and the only necessary triple coons should be there. Procedure import geometry. delete half side of car. clear the single cons and triple cons. assign PID's. Perform meshing with given quality criteria and target length. clear off elements.…

Aim: To check the geometrical errors and delete surfaces which are unwanted for surface wrap. and merge all 3 models and perform surface wrap. engine gearbox transmission Given target length: 3mm Procedure import geometry. delete unwanted parts. create surfaces to close geometry. merge all parts. start surface wrapping.…

Aim: To check and solve all geometrical errors and assign appropriate PID's. and perform meshing with suitable quality criteria and mesh parameter. import geometry Apply topo on the whole model Now most of the single coons will become Double coons. Now try using fill hole option where single coons are present. After filling…

Aim: To write a program to simulate the forward kinematics of a 2R robotic arm. Matlab code clear all close all clc l1 = 1;%length of arm 1 l2 = 0.5;%length of arm 2 theta1 = linspace(0,90,10);% angle variation for arm 1 theta2 = linspace(0,90,90);%angle variation for arm 2 ct = 1; %initialization of ct to capture animation…

Aim: To write a program that solves the following ODE. Mathematical calculation `(d theta)/(dt) = theta_1` `(d theta_1)/(dt) = theta_2` `(d^2theta_2)/(dt^2) =(d theta_1)/(dt)`  substituting these values in the main equation of Pendulum we wil get `(d theta_1)/(dt)+b/mtheta_1+g/Lsintheta = 0` Matlab code Function code…

Aim: to write a function to extract the 14 coefficients from NASA thermodynamic data.and calculate enthalpy, entropy and specific heat for all species. also calculate the molecular weight of each species. Given equation `(Cp)/R = a_1+a_2*T+a_3*T^2+a_4*T^3+a_5*T^4` `H/(RT) = a_1+(a_2*T)/2+(a_3*T^2)/3+(a_4*T^3)/4+(a_5*T^4)/5+a_6/T`…

Aim: To write a code to optimize the stalagmite function and find the global maxima of the function. Theory           A genetic algorithm is a search experiential that is stimulated by Charles Darwin’s theory of natural evolution. This algorithm reproduces the process…

Aim: To set up the channel flow simulation in converge. Objective: Run the simulation for the following mesh grid size.   dx(m) dy(m) dz(m) case-1 2e-4 2e-4 2e-4 case-2 1.5e-4 1.5e-4 1.5e-4 case-3 1e-4 1e-4 1e-4 Channel flow Flow in conduits or channels are of two types. Open channel flow: River, tidal currents, irrigation…

Aim: to simulate the flow over a backward facing step using converge. Objective: Run the case for three different base mesh sizes dx=dy=dz=2.0e-3m dx=dy=dz=1.5e-3m dx=dy=dz=1.0e-3m   Case setup 1. import geometry in converge 2. Assign triangles to a specified boundary Inlet outlet Top bottom wall Front_2d back_2d…

Aim: to setup and run the steady state simulation for flow over throttle body. Geometry  Import geometry extract the internal volume Close the openings Assign boundaries Inlet Outlet Elbow wall Throttle Check diagnosticsEverything seems perfect as per diagnostic result. Case setup Application type: Time based Materialsgas…

Aim: to setup and run the transient state simulation for flow over throttle body. Geometry  Import geometry extract the internal volume Close the openings Assign boundaries Inlet Outlet Elbow wall Throttle Check diagnosticsEverything seems perfect as per diagnostic result. Case setup Application type: Time based Materialsgas…

Aim: Simulate the prandtl meyer shock flow in converge CFD. Objective To Do a literature search on what BC's are typically used for shock flow problems. What is a shock wave? To describe the physics behind shock wave. Effects of SGS parameter on shock location (Sub-grid-scaling). Shock flow boundary conditions Boundry…