Multivariate Newton Raphson Solver for ODE s

Aim: To apply Reynold's decomposition to the Navier Stoke's equations to obtain the expression for Reynold's stress. Also understanding the terms Reynold's stress and the difference between turbulent and molecular viscosity. Theory: Most of the engineering problems deal with turbulent flows. A characteristic feature of…

Aim: To set up a transient shock tube simulation using Converge. Theory: Shock tubes are devices used for studying the flow of high temperature and high-velocity compressible gas. High-temperature supersonic gas flow is initiated in a shock tube as a result of the rupture of a diaphragm which is separating two gases…

Aim: To set up a flow simulation through a pipe for visualizing conjugate heat transfer through a solid pipe over the walls. Also, perform a grid dependence test and analyzing the effect of supercycle interval. Theory: Conjugate heat transfer (CHT) is a combination of heat transfer in solids and fluids. In solids,…

Aim: To simulate the Prandtl Meyer shock problem and check the effect of SGS temperature value on cell count and shock location using Converge. Also, perform a literature review on flow boundary conditions used for shock flow problems. Theory: We need boundary conditions in order to solve ordinary differential equations…

Aim: To perform a transient simulation a flow over a Throttle body using Converge. Theory: A throrttle valve is used to obstruct the fluid flow in IC engine in order to increase or decrease the power of the engine by restricting air-fuel mixture flow.A throttle valve represents a disc like device  positioned inside…

Aim: To perform a steady state simulation of flow over a Throttle body using Converge. Theory: A throrttle valve is used to obstruct the fluid flow in IC engine in order to increase or decrease the power of the engine by restricting air-fuel mixture flow.A throttle valve represents a disc like device  positioned inside…

Aim: To simulate a flow of a fluid in a channel using Converge for different mesh sizes. Theory: Channel flow is a branch of hydraulics and fluid mechanics, is a type of liquid flow within a closed conduit. The other type of flow within a conduit is open channel flow. Usually, an open channel flow has a free surface which…

Aim : To write a code to find 10 most sensitive reactions out of all the reactions in GRI 3.0 mechanism. Theory: A chemical mechanism represents all the reactions taking place in detail in order to achieve an overall global reaction. For a combustion process to take place there involves thousands of intermediate reactions.…

Aim : To write a code for calculating Autoignition time for methane combustion under various operating conditions using Cantera.  Theory: Autoignition occurs when a mixture of gases or vapours ignite spontaneously at certain operating condition without any influence of external ignition sources. The autoignition temperature…

Aim : We will be solving the below given coupled non-linear equations using Multivariate Newton Raphson method. Theory : From the above set of differential equations we can see that there are interdependent variables and these kind of problems are termed as coupled in nature. In order to solve these kind of coupled problem…

Aim : To analyse the flow pattern of the fluid inside a gear box. Theory: Gearbox is one of the vital component of vehicles and industrial machineries. It usually serves as a protection for the gears and also helps in providing lubrication for these gears. Lubrication is very much required for efficient working of these…

Aim : To study the stability of an Ordinary Differential Equations (ODE\'s). When does a ODE become unstable? Stability : Stability theory adresses the stability of solutions of differential equations and trajectories of dynamic systems under small pertubations of the initial conditions. If we consider a ordinary differential…

Aim : To derive the reaction rate Ordinary Differential Equations (ODEs) for a given reaction Mechanism. Rates of reaction for Multistep Mechanism: Usually mechanisms consist of 100s of species and 500s of reaction or in some cases even higher number of species and reactions. In this case we are considering a four step…

Aim : To understand the effect of pre-heating on Adiabatic Flame Temperature and Combustion Efficiency. Theory: Recuperator: A Recupeartor is a special purpose counter-flow energy recovery heat exchanger positioned within the supply and exhaust air streams of an air handling system, or in the exhaust gases of an industrial…

Aim : We will be using the Quantity Class of Cantera to create various mixtures and explaining how mixture calculations is performed. 1. Use the \"moles\" method/function of the A object and explain how it was calculated. In this process we will be considering a mixture of Methane and Air. `CH_4+2(O_2+3.76N_2) rarr CO_2+2H_2O+7.52N_2`…

Aim : To study the effect of equivalence ratio on Adiabatic Flame Temperature using Newton Raphson method and Cantera. To calculate the Adiabatic Flame Temperature for the constant pressure with heat loss. To calculate the Adiabatic Flame Temperature for various fuel types such as alkanes, alkenes and alkynes.  To…

Aim : To perform a parametric study on the gate valve by setting 5 different design points for the gate valve lift. Theory : Gate valves are used to shut off the flow of liquids rather than for flow regulations. When the valve is fully open, it has no obstruction in the flow path resulting in very low flow resistance.…

Aim : To perform a combustion simulation  on the combustor model and to plot the mass fraction of different species at different location inside a combustor. Theory : Combustion is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that…

Aim : To perform Numerical Analysis on a cyclone seperator by using different boundary conditions and to perform a grid dependency test for varying the number of particles inside the cyclone seperator. Theory : Cyclone Seperators are seperation devices which uses the principle of inertia to remove particulate matter from…

Aim: To perform Rayleigh Taylor Instability simulation for 3 different mesh Sizes. Theory: Rayleigh Taylor Instability is the instability at the interface between two fluids having different densities in hydrostatic equilibrium under acceleration. The lighter fluid pushes the heavier fluid which would result in the formation…

Aim : To perform a Conjugate Heat Transfer (CHT) Analysis on a Graphics Card. Theory : Conjugate Heat Transfer (CHT) Analysis: Conjugate Heat Transfer analysis is used for the processes that involve variation of temperatures with respect to solids and fluids, due to thermal interaction between them. A typical example would…

Aim : To perform a Conjugate Heat Transfer (CHT) Analysis for an exhaust manifold of an IC Engine. Theory : Why and Where a CHT analysis is used? Conjugate Heat Transfer analysis is used for the processes that involve variation of temperatures with respect to solids and fluids, due to thermal interaction between them.…

Aim : To perform a numerical analysis on flow over Ahmed body and to perform a grid dependence test. Theory : Ahmed Body and its significance: Ahmed Body is a simplified 3 dimensional representation of a passenger car. It was first designed by S.R.Ahmed in his research \"Some Salient Features of the Time-Averaged…

Aim : To simulate a 2D laminar flow over a cylinder using steady state and transient mode. Also to visulaize vortex shedding and determine the frequency of the vortex shedding to calculate Strouhal Number (Sr). Theory : Vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past…

Aim: To perform steady state simulations for analysing the mixing effectiveness of fluilds in a T-joint. Theory: The solid model we will be using for the simulation is a T-joint. It consist of 2 inlets and 1 outlet. The inlet is perpendicular to each other at a certain distance. These kind of pipes are usually used to…

Aim : In this project we will be simulating a flow through a pipe in openfoam using symmetry boundary condition.  Theory : Entrance Length refers to the distance in which the fluid travels afters entering a pipe before the full development of the flow. When the boundary layer expands to fill the entire pipe the developing…

Aim : To simulate a flow through a pipe using icoFoam solver in OpenFoam. A section of pipe (wedge-shaped geometry) is selected for the simulation to reduce is computational time. Theory : Entrance Length refers to the distance in which the fluid travels afters entering a pipe before the full development of the flow. When…

Abstract : In this project we will be designing various parts required for a 6-cylinder engine using solidworks. The type of cylinder arrangement we will be designing is a V-motor (Figure 1). There are many parts involved in operations of an engine. Some of the major parts are engine block, cylinder block, piston,…

Aim : To describe the need for interpolation schemes and flux limiters in Finite Volume Method (FVM). Theory : In computational fluid dynamics (CFD) there are 3 commonly used numerical method based solvers to solve the governing equations i.e Navier Stokes Equations. These 3 methods are: Finite Difference Method : …

Aim : To create a geometry for incompressible cavity flow problem in openfoam and to simulate the flow through a backward facing step for different grading factor using icoFoam solver. Geometry : The below figure is the geometry we will be creating in openfoam.   Mesh Specifications : Number of cells along the x direction…

Aim : To solve the 1D supersonic nozzle flow equations using the Macormack Method. Theory : We are considering a flow through convergent-divergent nozzle. A nozzle is a pipe or a tube with varying cross sectional area which can be used to direct or modify the fluid flow. Nozzles are commonly used to control the rate of…

Aim : To model a Boeing-747 aircraft using Solid works. Design Methodology : Step 1: To model the aircraft we make use of the blueprints containing Front view, Side view and Top view. These are oritented in the 3 basic planes using the appropiate dimensions from the drawing. Finally we make the sketch picture transparent…

Aim : To solve 2D Heat conduction equation in steady state and unsteady (Transient) forms using implicit and explicit techniques. 1) Steady State Solution (Implicit technique): Jacobi Method. Gauss Siedel Method. Successive Over relaxation Method. 2) Transient State Solution: Explicit Method. Matrix Inversion(Implicit).…

Aim : To compare and compute fourth order approximation of second order derivative using central differencing technique, skewed right sided difference technique and skewed left sidded difference technique using Taylor\'s Table method. Theory : The idea behind discretization is we get solution only at a discrete point.…