Deriving fourth (4th) order approximations of second-order derivatives Fourth-order approximation of second-order derivative using central differencing, Consider numerical stencil below for central differencing scheme,      The hypothesis equation for CDS is,            …

1.Steady State Analysis: - 2D Steady-state heat conduction equation is, `(delta ^2T)/(delta x^2)+(delta ^2T)/(delta y^2) = 0` using central differencing scheme we get, T(i,j) = `(Deltax^2Deltay^2) /(2(Deltax^2 + Deltay^2)) * [ (( T(i-1,j) + T(i+1,j))/(Deltax^2))+(( T(i,j-1) + T(i,j+1))/(Deltay^2))]` Matlab Program:- …

                   Simulation of 1D supersonic nozzle flow using McCormack’s Method   Objective: -       1.Simulation of 1D supersonic nozzle flow using McCormack’s Method. To plot variation in flow field variables in both Non-Conservative…

Finite Volume Method: - The finite volume method (FVM) is a discretization technique like FEM and FDM used in CFD. FVM evaluates the variables at discrete locations (center of the cell) of the geometry under consideration. FVM divides the geometry into a finite number of volumes (by forming mesh/grid). This mesh can be…

Obejective :  1. To calculet flow Variables. 2.To create blockMeshDict file using MATLAB  3.To simulate the pipe flow in OpenFOAM using icoFoam solver. 4. To compare the simulation and analytical resultsobtained using Hagen-Poiseuille equation. Enrtrance Length: Entrance length is the distance a flow travels after entering…

Objective:- 1.To write MATLAB codefor symmetry boundary conditions of flow through pipe. 2. To Simulate the pipe flow for 10, 25 and 45 degree angles.  3.To comapre results of wedge boundary condtions with symmetry boundary conditions. MATLAB Program:-  clear all close all clc D = 0.005; r = D/2; L =210*D; Re…

Objective:-  To simulate the air flow in Mixing Tee and understand the effect of length of pipe and momentum ratio of velocity for mixing air by four different cases. Selection of Turbulence Model:-    We have to select one turbulenece model from k- epsilon and k- omega. As, k- epsilon model predicts well…

Objective: - To simulate Flow over a cylinder using unsteady and steady state solvers with different Reynold numbers. Theory: -   Vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined) body at certain velocities, depending…

Objective:-  1. Describe Ahmed's body and its importance. 2. Explain the reason for the negative pressure in the wake region.  3. Explain the significance of the point of separation.    Ahmed body:-  The Ahmed body is a general car body (a basic vehicle model). The airflow around the Ahmed body…

Conjugate Heat Transfer Analysis (CHT) :-  The Conjugate Heat Transfer (CHT) analysis type of CFD analysis, which perform the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them. In certain critical applications…

Rayleigh Taylor Instability:-       The Rayleigh Taylor Instability occurs when the interface between two fluids of different densities is such as, lighter fluid is pushing the heavier fluid upward. Initially, two horizontal immiscible fluids, with a sharp interface separating them, lie horizontally…

  Objective:-  To perform CHT analysis on the graphics card. Conjugate Heat Transfer (CHT) Analysis:- The Conjugate Heat Transfer (CHT) analysis type allows for the simulation of heat transfer within solid and fluid domains by exchanging thermal energy at the interfaces between them.…

Cyclone Separator: - Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators are one of many air pollution control devices known as pre-cleaners since they generally remove larger pieces of particulate…

Gate Valve:- A gate valve, also known as a sluice valve, is a valve that opens by lifting a barrier (gate) out of the path of the fluid. Gate valves require very little space along the pipe axis and hardly restrict the flow of fluid when the gate is fully opened. The gate faces can be parallel but are most commonly…

Combustion: - Combustion or burning is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually, atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a…

Adiabetic Flame Temperature:- When a combustion reaction takes place energy is liberated to the combustion products. If no heat is lost in this process, the temperature of the combustion products is known as the "Adiabatic Flame Temperature." This is the maximum temperature that can be reached for given reactants. …

Objective:-  To calculate adiabetic flame temperature of the gas mixture using the quantity of class. Python code for calculation mass and mole fraction of air:- """ Python code for calculation mass and mole fraction of air """ import cantera as ct gas = ct.Solution('gri30.xml') air = ct.Quantity(gas) air.TPX = 298.15,ct.one_atm,{'O2':0.21,…

Theory:-     Recuperator is a type of heat exchanger that has separate flow paths for each fluid along its passages and heat is transferred through the separating walls. Recuperators are usually used in power engineering, to increase the overall efficiency of thermodynamic cycles. For example, in a gas turbine engine.…

Objective:- To derive the reaction rate ODE of a simple reaction mechanism. considering given reactions,              List of all species of hydrocarbons that are taking place in the reaction 1.O2 2.H2O 3.CO2 4. OH 5. CO 6. H 7. O Defining `upsilon underset(i j')`be the stoichiometric…

  1. When does an ODE become unstable? To find the unstable condition for an ODE let's assume an equation for ODE and run the program for various dt.                                                …

AIM:- This project aims to solve the system of ODE using the Newton-Raphson method.   Python Program:- """ This python program is written to solve a system of coupled non-linear equations using multivariate Newton-Raphson solver dy1/dt = -0.04*y1 + 10^4*y2*y3 dy2/dt = 0.04*y1 - 10^4y2*y3 - 3.10^7*y2^2 dy3/dt = 3.10^7*y2^2…

 Aim:- To find the autoignition time of methane under varying conditions of pressure & temperature and analyze the evolution of molar concentrations of reactants with combustion progress. For this, we will consider:   Case -1: Auto-ignition time with A. Constant temperature of 1250 K and pressure variation from 1 to 5…

Aim:- The aim is to find the sensitivity with respect to the temperature from the GRI mechanism by taking all the reactions and calculating the 10 most sensitive reactions.   Sensitivity Theory:-   Sensitivity analysis is the study of the change of the dependent variable with respect to the independent variable.      …

Objective:-  Simulating forward kinematics of a 2R Robotic arm using MATLAB program. Theory:- A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. The links of such a manipulator…

Objective:-  To solve a second-order ODE of a simple pendulum and create its animation. Theory:-   ODE represents the equation of motion of a simple pendulum with damping: -                                      (d^2 θ) / dt^2+ (b/m)*( dθ/dt)+(g/L)*sinθ = 0   .......Equation-1 Simplifying the above ODE: -              …

Objectives: - 1. Write a code in MATLAB to optimize the stalagmite function and find the global maxima of the function. 2. Explain the concept of genetic algorithm and also explain the syntax for ga in MATLAB. 3. Plot graphs for all 3 studies and F maximum vs no. of iterations.   Theory: -  …

Aim – To parse a data file and plot the required properties by calculation. Objectives – To extract the 14 coefficients and calculate the specific heat, entropy, and enthalpy for all species in the data file. To calculate the molecular weight of each species. To plot Specific heat, Enthalpy, and Entropy…

Rankine Cycle SimulatorAim:Creation of Rankine cycle simulator from given input and reading the data from a standard thermodynamic library of steam table.Objective: To create a Rankine Cycle simulator in MATLAB. To calculate the state point using the function XSteam. To plot the T-S and H-S curve for a given input in the…

AIM :To generate surface meshing for the pressure valve geometry for 3 different target mesh lengths.OBJECTIVES :1. To check for geometrical errors and perform Topology clean-up for the given model.2. Set three different target lengths as three different cases and mesh the model.  Target…

AIM:For the given model, to check for the geometrical errors to make appropriate volumes, create and assign PIDs. To perform surface mesh with the given target lengths as per PIDs. Blade stage-1 = 1 mm Blade stage-2 = 1 mm Impeller = 2 mm Shaft rotor = 1 mm Turbo casing = 5 mm Compressor casing = 5 mm Inlet casing cover…

Objective:-To clean up the given car model and perform surface meshing for the given mesh lengths and create a wind tunnel around the car with surface mesh and volumetric mesh for volume in the tunnel surrounding the car.PROCEDURE :- The first step is to import the geometry and run a geometry check. Using the geometry…

AIM : To perform surface wrap on automotive assembly in ANSA. OBJECTIVES :  To do the Geometry Preparation using TOPO Tools in ANSA To perform surface wrapping of the Geometry for the CFD with target length of 3mm.  INTRODUCTION :Surface wrapping in CFD meshing is used to create a simplified,…

AIMClean up the given model and perform surface meshing first and then volumetric meshing for the relevant volume.PROCEDURE The first step is to import the geometry and run a geometry check. As this geometry has fewer corrections, we will directly move to TOPO cleanup and instead of using the symmetry method. Using the…

I. INTRODUCTION Channel flow is an internal flow in which the confining walls change the hydrodynamic structure of the flow from an arbitrary Mote at the channel inlet to a certain state at the outlet The simplest illustration of internal flow is a laminar flow in a circular tube, while a turbulent flow in the rotor…