Deriving fourth order approximations for second order derivative: 1. Central differencing : In central differencing scheme, we take in consideration two grid points on the left side and two gid points on right side. we can rewrite our second-derivative as `delta^2 x//delta x^2 = a *f(i-2) + b* f(i-1) + c*f(i) + d*f(i+1)…

1. Steady State Analysis: Solving the 2D heat conduction equation by using the point iterative techniques that were taught in the class. The Boundary conditions for the problem are as follows; Top Boundary = 600 K Bottom Boundary = 900 K Left Boundary = 400 K Right Boundary = 800 K The steady state heat equation can be…

In this problem isentropic flow through a convergent-Divergent nozzle is shown in the figure below. The flow at the inlet to the nozzle comes from a  reservoir where the pressure and temperature are denoted by p0 , and To, respectively. The cross-sectional area of the reservoir is large , and hence the velocity…

In this challenge, the objective was to simulate an incompressible-laminar-viscous flow through the backward facing step geometry, transient simulation is performed. The openFoam software tool was used in ubuntu OS.  OpenFOAM (for "Open-source Field Operation And Manipulation") is a C++ toolbox…

The finite volume method (FVM) is a discretization technique for partial differential equations, especially those that arise from physical conservation laws. FVM uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations. FVM is in common use for discretizing…

In this challange the main objectives are- Write a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading schemes For a baseline mesh, show that the velocity profile matches with the Hagen poiseuille's equation Show that the velocity profile is fully developed Post…

This challange is the continuition of the Simulation of the flow through pipe in openFoam but the difference in this challange is that we have used the angle as 10deg, 25deg and 45deg for the wedge, and on the above of it the front and back face are of the type wedge and symmetry. So there are total 6 cases in this challange…

Mixing problems, such as the design and scale-up of a mixer and quantification of mixing, have been traditionally tackled by developing empirical design equations mainly due to the complexity of the fluid dynamics of mixing. Although this approach has proven to be satisfactory for many applications, it is rather limited…

The flow past a circular cylinder is associated with various instabilities. These instabilities involve the wake, separated shear layer and boundary layer. Williamson1 has given a comprehensive description of the flow phenomena at different Reynolds numbers (Re). Upto Re ∼ 47, the flow is steady with two symmetric…

The Ahmed body is a generic car body (a simplified vehicle model). The airflow around the Ahmed body captures the essential flow features around an automobile and was first defined and characterized in the experimental work of Ahmed [1]. Although it has a very simple shape, Ahmed body allows us to capture characteristic…

The Conjugate Heat Transfer (CHT) analysis type allows for the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them. Typical applications of this analysis type exist as, but are not limited to, the simulation of heat exchangers,…

The instability of a heavy fluid layer supported by a light one is generally known as Rayleigh-Taylor (RT) instability. It can occur under gravity and, equivalently, under an acceleration of the fluid systemin the direction toward the denser fluid.Water suspended atop oil is an everyday example of Rayleigh–Taylor…

The Conjugate Heat Transfer (CHT) analysis type allows for the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them. Typical applications of this analysis type exist as, but are not limited to, the simulation of heat exchangers,…

To write a few words about any four empirical models used to calculate the cyclone separator efficiency.    Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases Cyclone…

A gate valve controls the media's flow by lifting the gate (open) and lowering the gate (closed). A gate valve's distinct feature is the straight-through unobstructed passageway, which induces minimal pressure loss over the valve. The unobstructed bore of a gate valve also allows for a pig's passage in cleaning pipe procedures,…

Combustion phenomena consist of many physical and chemical processes which exhibit a broad range of time and length scales. A mathematical description of combustion is not always trivial, although some analytical solutions exist for simple situations of laminar flame. Such analytical models are usually restricted to problems…

Adiabatic Flame Temperature: For a combustion process that takes place adiabatically with no shaft work, the temperature of the products is referred to as the adiabatic flame temperature. This is the maximum temperature that can be achieved for given reactants. Heat transfer, incomplete combustion, and dissociation…

stoichiometric Equation for Methane combustion is- #MethaneCH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.5N2   Question 1. Use the "moles" method/function, calculate the number of moles of object A and explain how it is calculated analytically.  The formula for calculating mole fraction is   `X_(O2) = m_(O2)/(m_(O2)+m_(N2))`…

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 to the combustion process. A general flow diagram is shown in the figure below.                          …

A balanced equation for a chemical reaction indicates what is reacting and what is produced, but it reveals nothing about how the reaction actually takes place. The reaction mechanism (or reaction path) is the process, or pathway, by which a reaction occurs. A chemical reaction usually occurs in steps, although…

The term “Ordinary Differential Equations” also known as ODE is an equation that contains only one independent variable and one or more of its derivatives with respect to the variable. In other words, the ODE is represented as the relation having one independent variable x, the real dependent variable…

Solving the non-linear coupled equations.  The equations are given as: `(dy1)/dt= -0.04*y1 + 10^4*y2*y3` `(dy2)/dt = 0.04*y1 - 10^4*y2*y3 - 3*10^7*y2^2` `(dy3)/dt = 3*10^7*y2^2`   To solve the above set of equations jacobian and implicit Euler solver are used. Implicit Euler: For solving the equations backward…

Auto ignition Temperature: The autoignition temperature of a substance indicates the lowest temperature at which it may spontaneously ignite without the presence of an ignition source such as a flame or spark. At the auto-ignition temperature, the temperature alone provides sufficient energy to induce combustion. As the…

Senstivity Analysis Assignment Sensitivity analysis is defined as the process of making a relationship between the parameters and the output of the model.  The simple ODE for the effect of the reaction rate on temperature or species concentration is: `(dZ)/(dt) = F(Z,t,a)` `Z = (T, Y1, Y2, ....Yk)^T` where, Z is a…

AIM 1. For this challenge, we will be setting up a channel flow tutorial. 2. Once you have the base setup ready, run the case for three different base mesh sizes. 3 different base mesh sizes are,  dx = 0.001m,          dy = 0.001m,       dz = 0.001m  dx = 0.0005m, …

AIM 1. To set up a case of backward facing step in converge 3.0 software. 2. To use 3 different sizes of mesh for the problem. 3. Show the mesh (i.e surface with edges) for all the 3 base mesh sizes 4. Show pressure and velocity contours 5. Show the plots of velocity, pressure, mass flow rate and total cell count for all…

Aim: Set up and run the steady state simulation for flow over throttle body. Post process the results and show pressure and velocity contours. Show the mesh (i.e surface with edges) Show the plots for pressure, velocity, mass flow rate and total cell count. Introduction: The throttle body is an important part of the air…

Aim: Setup and run transient state simulation for flow over a throttle body. Post process the results and show pressure and velocity contours. Show the mesh (i.e surface with edges) Show the plots for pressure, velocity, mass flow rate and total cell count. Also show the calculations on how you calculated an end time for…

A centered, Prandtl-Meyer expansion wave is illustrated in Fig. below. Here, a supersonic flow is expanded around a sharp expansion comer. An expansion wave, made up of an infinite number of infinitely weak Mach waves, fans out from the comer, as shown in Fig. below. The leading edge of the expansion fan makes an angle…

The first stage of a modern gas turbine operates at very high temperatures so that an efficient cooling system is required to protect the vanes by the very hot gas. Designing an efficient turbine thus requires an accurate evaluation of the flow and temperature fields within the hot gas outside the vanes and of the cooling…

Shock tube is one of the simple laboratory apparatus that can generate various flow speeds at different flow regimes. The shock tube performance is based entirely upon the pressure ratio and speed of sound in driver and driven section. The strength of shock increases in the ratio of speed of sound.…

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence…

Objective: The objective of this work is to setup no hydro simulation of IC engine in converge CFD. Other work Includes boundary flagging and model setup for no hydro simulation. Modelling the problem in Converge Software The 3D model is imported in the software.  Each of the face is given a boundary name and allotted…

Aim: To set up the mesh on a Valve using ANSA Software. Procedure: Initially, the 3D model is imported in the software. Next, Geometry is checked for various issues related to open edges etc., in the checks manager. After geometry check-up, results are analysed which shows that single cons error, and it needs to be…

Aim:  CFD meshing on Turbocharger Procedure:  Initially, the 3D model is imported in the software. Single and triple cons are identified by usng geometry check. Empty spaces and single con are filled. The one case is shown below The remaining part is patched using the New Face option. The similar procedure…

Aim: To set up combustion simulation in an IC Engine in Full hydro using Converge. Objective: 1. What is the compression ratio of this engine? 2. Why do we need a wall heat transfer model? Why can't we predict the wall temperature from the CFD simulation? 3. Calculate the combustion efficiency of this engine 4. use the…

Objective:  1. Analyze two-piston bowl configurations (open-w and Omega) of CAT3410 engine. 2. Ananlyzing the emissions from the two confguraions. 3. Comparison of power and imep of the two piston profiles.   Geometry: This project uses 60 degree sector model of the CAT 3410 engine with two different piston profiles.…

Questions based on PFI Engine: Q1. What is the Compression ratio for the engine? The compression ratio is defined as the ratio between the volume of the cylinder with the piston in the bottom position, Vbottom (largest volume), and in the top position, Vtop (smallest volume). The higher this ratio, the greater will be…

Aim: To prepare the wind tunel meshing of BMW Car. In this project the avialable 3d model of the BMW car is cleaned and mesh is prepared for the external CFD simulation. A step by step procedure is shown below. The below image shows the raw model to be processed. As it can be seen that there is a lot of deformities and…

Aim: Surface wrap on the automotive assembly. Before going for the surface wrap all of the models are made free of losse surfaces outside the required zone along with closing of unnecessary open holes. Initial the Engine model is imported in the ANSA window and the raw model looks as the following. From the engine model…

Aim: To prepare the wind tunel meshing of Tesla Cyber Truck. In this project the avialable 3d model of the Tesla Cyber Truck is cleaned and mesh is prepared for the external CFD simulation. A step by step procedure is shown below. The below image shows the raw model to be processed. As it can be seen that there is a lot…

GT-SUITE is the industry-leading simulation tool with capabilities and libraries aimed at a wide variety of applications and industries. It offers engineers functionalities ranging from fast concept design to detailed system or sub-system/component analyses, design optimization, and root cause investigation.  …