Deraviation of 4th order approximations of the second-order derivative using various schemes:- The given function is  `exp(x)*cos(x)` The second derivative is :- `-2*exp(x)*sin(x)` 1. Central Difference Scheme:- As given, no. of Nodes (N) required for 4rth order approximation (P = 4) of 2nd order deravative (Q…

The governing equation for 2-D heat conduction is : 2-D Transient :- `{delT}/{delt} + alpha ({del^2T}/{delx^2}+{del^2T}/{dely^2}) = 0` where `alpha` is the thermal diffusivity of the medium.       Descritizing the above equation we get:- `{T_(i,j)^(n+1) - T_(i,j)^(n)}/{Deltat} + alpha*({{T_(i-1,j) -2*T_(i,j)…

Simulation of a 1D Super-sonic nozzle flow simulation using Macormack Method Schematic representation of convergent divergent nozzle. In the above described convergent divergent nozzle, while simulating for the flow parameters, an assumptions has been made that the flow property will only vary with x. Thus the uniform…

Simulation of a backward facing step in OpenFOAM  The project demonstrates importance of grading factor while meshing in CFD numerical simulation. Geometry for analysis:- In order to develop this geometry to be solved in openFoam, 3 blocks were made and meshed using blockMesh. The blocks created is described below:-…

Finite Volume Method:- It is one of the method for evaluation and representation of differential equations in form of algebraic equations. This method can be used on all differential equations which can be written in the divergence form. The integration is done over the volume. Applying gauss theorem, the volume integral…

Hagen- Poiseuille's equation Given Rynolds no. of 2100 assumed for water as a fluid is nearly laminar flow. When fluid elements enter a pipe, due to friction force at the boundary of the pipe the crosssectional velocity is non uniform. Fluid elements flowing near the boundaries has less speed as compared to the center…

Continuining from the previous challenge, the script creating the blockMeshDict file was used to get the file for 10, 25 and 45 deg wedge angle. The blockMeshDict creater script is as below:- % Matlab script for generating the blockMeshDict file given wedge angle clear all close all clc %% Properties declaration % User…

The Aim, Introduction, Theory Mixing tee is an important engineering component, primarily used in mixing of different fluids of different conditions to achieve desired properties. In the present study, mixing of air at different temperatures is simulated. The configuration has two inlet valves and one outlet valve. One…

Project Report - Flow over a Cylinder Introduction Flow past object, has been a topic of interest since long time. The phenomenon is very common in engineering designs. The complex nature of physics and behaviour of transport phenomenon around the object is still being actively studied. The nature of flow changes at critical…

Project Report Introduction Ahmad Body (car model) is a simplified vehicle model concept, primarily used in studying the aerodynamics of vehicle. The length of the model stands out to be 1.044m, the width is of 0.389m and height stands to be around 0.288m. It has 4 pillars for simulating wheels, the diameter of which is…

Project Report Introduction CHT or conjugate heat transfer, refers to a heat transfer process involving an interaction of conduction within a solid body and the convection between the moving liquid media and solid media. Heat transfer in the solid domain is primarily due to conduction, for the fluid domain, it is dominated…

Project Report Rayleigh Taylor Instability Introduction The Rayleigh–Taylor instability, also called RT instability is an instability at the interface between two fluid of different densities, when the lighter fluid is pushing the heavier fluid. The flow or turbulent mixing is the consequence of lowering the potential…

Project Report CHT Analysis on a Graphics card Introduction Graphic Card or GPU is an electronic component often a computer's pepheral, responsible for computing the graphic signals, later transmitted to a graphic device. It has various range of performance as well as power usage. based on the design, the power rating…

Simulating Cyclone separator with Discrete Phase Modelling Introduction Cyclone separator are an economical device for removing particulate solids from a fluid system. Particle along with a working fluid gets introduced via a stream through inlet, the induced centrifugal force is tangentially imparted on the wall of the…

Parametric study on Gate valve Introduction A gate valve, also called sluice valve, often installed in a pipe fitting, opens by lifting a barrier called 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…

Simulating Combustion of Natural Gas Objective Following are the objective of the present study: To perform a combustion simulation on the combustor model To add the water content in the fuel from 5% to 30% by mole and observe the effect of it on the results. Outline In order to achieve the above stated objective, the…

Adiabatic Flame Temperature calculation Introduction If no heat is lost in the process of combustion, the temperature of the combustion products is known as the Adiabatic Flame Temperature (AFT). As a rule of thumb, more the combustion products, much energy is distributed among the particles and temperature is relatively…

Combustion Efficiency Calculation after Preheating Introduction Recuperator is a device that acts as a heat exchanger by utilizing high temperature exhaust gas for heating the inlet air headed for combustion. Preheating the air without burning extra fuel is advantageous in combustion cycle. Objective: Explore the effect…

Handling Mixtures with Cantera Introduction Quantity is a defined class representing a specific quantity of a Solution. Class Quantity provides several additional capabilities. A Quantity object is created from a Solution with either the mass or number of moles specified Calculation of mole Mole fraction as per given in…

Objective: Deriving the reaction rate ODE of the given reaction mechaninsm using compact notation. Solution: Let the unique species in the set of reactions be identified by j index and the individual reaction be identified by i index. The Species are: Species CO `O_2` `CO_2` O `H_2O` OH H j-index 1 2 3 4 5 6 7 The reaction…

When does a ODE become unstable? When a solution to ordinary differential equation is approached by iterative numerical methods, the absolute error between iterations gives us an idea about the stability of the solution. For a stable solution, the error between the iterations should decrease. The step size in the iterative…

Newton Raphson Method: The generalized version of multivariate newton raphson method can be expressed as: `Y_{"new"} = Y_{"guess"} - alpha*(J^{-1}*F)` Where, J is the jacobian matrix F is the algebriac function Y is the solution vector   The given Differential Equation: `{dy_1}/{dt} = -0.04y_1 + 10^4y_2y_3` `{dy_2}/{dt}…

Introduction: Ignition delay is the time interval during which it takes from ignition temperature to 400K above it. `Time_{"ignition delay"} = Time_{"initial temperature + 400K"}` In the present work variation of ignition delay with pressure and temperature has been studied. Objectives : - Study the variation of Auto Ignition…

Introduction: Sensitivity analysis given an overview of magnitude of variation of an independent variable over dependent variable. It is the study that helps in investigation of factors that has the potential to alter the given outcome. Since our study is focussed on the chemical reactions, the reactants and their initial…

Channel Flow Simulation using Converge CFD Introduction: Flow through channel is a common phenomenon observed in many engineering applications. The physics of flow in a channel or a closed boundary can be best described by the forces governing the cause of flow i.e., energy gradient and friction encountered at the boundary…

Flow over a backward facing step Introduction   Many engineering application such as aerodynamic flows, engine flows, condensers, vehicles, heat transfer systems, and flow around buildings etc. involves flow separation and reattachment. Backward-Facing Step is a representative model for domenstrating separation flows.…

Steady state simulation of flow over a throttle body   Introduction Throttle is a mechanism often coined in relative to flow of fluids, responsible for controlling its flow across the pipe, by constriction or obstruction. The present study is about a butterfly throttle that uses obstruction to control flow of air…

Transient Simulation of Flow Over a Throttle Body Introduction Throttle mechanism is often used as a measure of controlled flow of fluid. It is one of the mechanisms that uses obstruction in flow path of fluid. Objective To set-up steady state simulation of flow over a throttle body. The channel of flow is a circular pipe…

Prandtl-Meyer Shock Simulation Introduction Movement of object through gas causes its molecules to deflect. Given the speed of the object is less than the speed of sound in the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum and energy. As the speed of the objects…

Conjugate Heat Transfer Simulation Introduction CHT or conjugate heat transfer, refers to a heat transfer process involving an interaction of conduction within a solid body and the convection between the moving liquid media and solid media. Heat transfer in the solid domain is primarily due to conduction, for the fluid…

Shock Tube Simulation Introduction Explosion is a physical phenomenon in which chemical energy is transformed into very wide pressure gradient or shock waves. It is a very active research subject in various field. Among many such fields, study of explosion in a pipe is very commonly pronounced in automotive industry. Pipe,…

Need of Turbulence Modelling Accurate solution of turbulent phenomenon requires much finer grid size. The trivial process would require huge computational resources. Thus, in order to arrive approximate results, time averaging convept is used to solve the turbulent phenomenon. RANS or Reynold averages Navier Stokes model…

Project 1 - Surface preparation and Boundary Flagging (PFI) Introduction An internal combustion engine is a heat engine in which the combustion of a fuel occurs in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal combustion engine, the expansion of the high-temperature and…

Objective:- Simulate PFI - engine in Converge CFD Geometry The prepared geometry from the previous section has been used in the present simulation. Simulation Type of Simulation  Crank angle-based IC engine simulation The given parameters were,  RPM of 3000 Connecting rod of length 0.18m Stroke of length 0.09m…

Emission characterization on a CAT3410 engine Objective To simulate the CAT 3410 engine using diesel fuel and characterize the emission for open W piston and Omega Piston. Simulation The geometry has been modified making it less heavy computationally. The given geometry has been transformed for sector simulation of 60deg.…

Project Report - Flow over a Cylinder Introduction Flow past object, has been a topic of interest since long time. The phenomenon is very common in engineering designs. The complex nature of physics and behaviour of transport phenomenon around the object is still being actively studied. The nature of flow changes at critical…

Detailed Objectives and Motivation Flat plate heats sinks are most common cooling solution for low to medium heat dissipating electronic equipment. Its ease in manufacturing attracts diverse range of material selection with required thermal properties. Selection of material is not the only part and parcel in manufacturing…