Introduction and application of finite volume method (FVM) for 1-D linear heat conduction equation

INTRODUCTION: Flame speed is the measured rate of expansion of a flame front in a combustion reaction. While the auto-ignition temperature and ignition delay (0-D analysis) can indicate when the reaction will take place, the flame speed (1-D analysis) is an indicator of how the flame propagates. The flame occupies a small…

INTRODUCTION: In this project, we will be simulating a 2-D flow through a rectangular channel. The size of the mesh will be varied (from coarse - fine - very fine) to compare the results. The setup is done using CONVERGE Studio and the results are post-processed in Paraview. The geometry is a simple box (channel) with…

SURFACE PREPARATION: CONVERGE CFD utilizes geometry provided in the ".stl" format, which contains a triangulated surfaces that make up the body. The geometry of the PFI engine is provided with certain geometrical errors. Some of the errors are and the methodology to correct them are listed below: 1. Intersections This…

INTRODUCTION: Auto-ignition occurs when a mixture of gases or vapors ignites spontaneously in absence of any external ignition source such as a flame or a spark. The temperature at which auto-ignition occurs is called the auto-ignition temperature. It is the lowest temperature in a system where the rate of heat evolved…

INTRODUCTION: Conjugate heat transfer (CHT) studies are performed when simulating heat transfer through both a fluid and a solid medium. For a fluid medium, the convective heat transfer is dominant while for a solid medium, the conductive heat transfer is dominant. The time required to attain the steady-state varies drastically…

INTRODUCTION: Lubricants are essential for the long-term smooth functioning of gearbox systems. In this project, we will visualize the gearbox sloshing effect to see how the lubrication is affected by different models of the gearbox (low and high clearance) as well as by using different fluids as lubricants. In total,…

INTRODUCTION: In the study of combustion, there are two types of adiabatic flame temperature (AFT) depending on how the process is completed: the constant volume and constant pressure; both of which describe temperature that combustion products theoretically can reach if no energy is lost…

INTRODUCTION: Most of the spark ignited internal combustion engines use a throttle valve to control the flow of fuel and air in order to maintain the desired air-to-fuel ratio. In this project, we will study the flow of air over a standard `90^0` elbow containing a throttle valve which rotates from `0^0` to `25^0` gradually…

INTRODUCTION: Ordinary Differential Equations (ODEs) can be solved through various numerical methods, including numerical discretization and numerical integration. Some ODEs can be solved directly through mathematical integration. However, most practical phenomena contain a system of ODEs and PDEs which may be coupled…

INTRODUCTION: Taylor series is used to approximate the values of derivatives at a certain node through various approximation schemes. The derivative at a node is measured with the help of the data at the surrounding nodes. These approximations produce some errors in the calculations which are dependent on the spacing between…

INTRODUCTION: Shock-tubes are widely used to study the ignition delay for a particular reaction. The process involves two stages: Two reactants are kept separate from each other in different regions, separated by a diaphragm, one at a very high pressure and one at low or atmospheric pressure. The diaphragm is suddenly…

INTRODUCTION: This project deals with a quasi 1-dimensional flow through a convergent-divergent nozzle. The governing equations for the flow can be written in two forms - (1) Conservative, and (2) Non-conservative. Both the conservative and non-conservative forms of the equations resemble the exact same thing and are interchangeable.…

INTRODUCTION: The Ahmed body is a standard model of a generic car shape used as a reference for wind tunnel testing of road vehicles. The characteristic feature of the structure is the slant plane in the rear side of the body which contributes to flow separation and recirculation in the wake region of the flow. Experimental…

INTRODUCTION: In this project, we will be simulating an incompressible laminar flow through a cylindrical pipe in OpenFOAM using the icoFoam solver. Instead of simulating the entire cylindrical pipe, we will be geometrically reducing the model to save computational resources. The geometry will only contain a slice of the…

INTRODUCTION: Rayleigh-Taylor instability occurs at the interface of two fluids of different densities when there is mixing due to the lighter fluid pushing the heavier fluid under the influence of gravity. Examples include water suspended in oil, mushroom clouds formed by volcanic eruptions or nuclear explosions, instabilities…

INTRODUCTION: Processors and graphics cards are widely used in computers today. As the functionality of the computers keeps on increasing, more and more power is required to keep up with the computational powers. A graphics card consists of three major components - the processor, the processor base and the cooling mechanism.…

INTRODUCTION: In this challenge, we will solve the following 1D linear convection equation to observe the propagation of a square wave with time. `{partial u}/{partial t} + C {partial u}/{partial x} = 0` Here, `C` is the velocity of propagation. The above equation is discretized using first-order forward differencing…

INTRODUCTION: When a gas is flowing at subsonic speeds (slower than the speed of sound), the density of the gas can be assumed as constant throughout the doman. However, when a gas is flowing at supersonic speeds (faster than the speed of sound), the density of the gas changes locally as it gets compressed or expanded.…

INTRODUCTION: In any particular reaction mechanism, there are multiple intermediate reactions happening which affect the rate of the entire mechanism. These reactions depend on different operating conditions and can be controlled to alter the mechanism to the desired state. In order to control the reactions, we can change…

INTRODUCTION: A reaction mechanism is a step-by-step sequence of elementary reactions by which overall chemical change occurs. It helps to study the different stages of a chemical reaction in detail. Obtaining an accurate mechanism for a given set of conditions is very challenging. Different conditions affect the reaction…

INTRODUCTION: While solving a combustion mechanism, the rates of production/depletion of different species are calculated in the form of ordinary differential equations (ODEs). The rate of production/dissipation of a particular species depends on the concentration of the species itself as well as the concentration of other…

INTRODUCTION: In this project, we will be simulating flow through a tee joint to analyze the mixing and the heat transfer. A tee joint is formed when two members are connected perpendicularly to each other. The tee joint has a variety of applications. In plumbing applications, it is used to direct the flow in one direction…

INTRODUCTION: In this project, we will be focusing on a laminar pipe flow simulation for a geometrically reduced model with two boundary conditions - wedge and symmetry. The pipe is reduced to a section with a central angle as shown below. The flow is to be simulated at `Re = 2100` with the fluid as water. We assume a…

INTRODUCTION: Most of the spark ignited internal combustion engines use a throttle valve to control the flow of fuel and air in order to maintain the desired air-to-fuel ratio. In this project, we will study the flow of air over a standard `90^0` elbow containing a throttle valve which is in a fully open position.  …

INTRODUCTION: A recuperator is a special purpose counter-flow energy recovery heat exchanger connected with the furnace positioned in the exhaust gas-streams in order to recover the waste heat. One use of a recuperator is to preheat the air entering the combustion chamber before mixing with the fuel. A schematic of the…

INTRODUCTION: A gate valve is a valve that opens by lifting a barrier (gate) out of the path of the fluid. They require very little space and do not restrict the flow when fully opened. In this project, we will be analyzing a simple pipe flow by varying the lift of the gate valve and observing the output flow rate. We…

INTRODUCTION: In this project, we will be simulating a two-dimensional flow over a cylinder to visualize the von Karman vortex street. The von Karman vortex street is caused by vortex shedding due to the unsteady separation of flow around a blunt body. The vortex shedding effect is caused only for a particular range of…

INTRODUCTION: A reaction mechanism includes several reactions occurring within a system. The rates of production/depletion of any species in the reaction can be modeled as an ordinary differential equation (ODE). The rate of production of a species depends on the concentration of that species as well as on concentrations…

INTRODUCTION: Conjugate heat transfer analysis allows us to study the heat transfer between a solid body and a fluid at the interface. The CHT analysis is governed by the set of governing equations consisting of conformity with the physical pattern of two separate systems for the solid and fluid domains. These equations…

Introduction: In this project, we are going to solve the equation of motion for a simple damped pendulum which is represented by the following ordinary differential equation (ODE): `{d^2\\theta}/{dt^2} + b/m{d\\theta}/{dt} + g/Lsin\\theta = 0` In the above equation, `\\theta` represents the angular displacement of…

INTRODUCTION: Finite volume method (FVM) is a method of solving the partial differential equations in the form of algebraic equations at discrete points in the domain, similar to finite difference methods. The difference between the two is that the finite difference method is evaluated at nodes, whereas the finite volume…

INTRODUCTION: When a gas is flowing at subsonic speeds (slower than the speed of sound), the density of the gas can be assumed as constant throughout the doman. However, when a gas is flowing at supersonic speeds (faster than the speed of sound), the density of the gas changes locally as it gets compressed or expanded.…

INTRODUCTION: In this project, we will be solving the incompressible laminar Navier-Stokes equation using the icoFoam solver for a pipe flow over a backward facing step. The results for different near-wall mesh grading factors are compared. Different inlet velocities are also used to compare the separation and reattachment…

INTRODUCTION: Cyclonic separation is widely used in the industry to remove particulates from an air, gas or liquid stream, without the use of filters, through vortex separation. Rotational effects and gravity are used to separate a mixture of solids and fluids. A high speed rotating airflow is established within a…

INTRODUCTION: The 2-D heat conduction equation is a partial differential equation which governs the heat transfer through a medium by thermal conduction. The equation is defined as: `{partial T}/{partial t} = alpha[{partial ^2T}/{partial x^2}+{partial^2T}/{partialy^2}]` For the steady state, the temperature does not vary…

INTRODUCTION: For a system of linear equations, the solution can be found by implementing the iterative solvers (Jacobi, Gauss-Seidel, and SOR). However, there are some factors which can render the solution unstable. One of these parameters is the spectral radius of the iteration matrix. The spectral radius of a matrix…

INTRODUCTION: Combustion is a high-temperature exothermic redox chemical reaction between a fuel and an oxidant, that produces oxidized, often gaseous products, in a mixture termed as smoke. Complete combustion is almost impossible to achieve since the chemical equilibrium is not necessarily reached, or may contain unburnt…

INTRODUCTION: For a high Reynolds' number flow, the flow is no longer laminar. The Navier Stokes equations cannot be used to characterize the flow. For this purpose, Reynolds' Averaged Navier Stokes (RANS) equations are derived which are obtained by averaging the Navier Stokes equations to account for the turbulence fluctuations…

INTRODUCTION: The backward facing step is a standard problem for validation of a computational fluid dynamics code. The problem is a simple rectangular channel whose cross-sectional area increases instantaneously which produces a variety of interesting flow features. The geometry and the flow features of interest are shown…

INTRODUCTION: In this challenge, we will solve the following 1D linear convection equation to observe the propagation of a square wave with time. `{partial u}/{partial t} + C {partial u}/{partial x} = 0` Here, `C` is the velocity of propagation. The above equation is discretized using first-order forward differencing…

For the combustion of methane in air, we know that the ideal reaction must be: `CH_4 + 2(O_2 + 3.76N_2) rarr CO_2 + 2H_2O + 7.52N_2` Generally, the air and fuel are mixed at the same conditions before entering into the furnace. However, sometimes they are mixed at different conditions. One such condition includes preheating…

INTRODUCTION: In this project, we will be simulating a 2-D flow through a rectangular channel. The size of the mesh will be varied (from coarse - fine - very fine) to compare the results. The setup is done using CONVERGE Studio and the results are post-processed in Paraview. The geometry is a simple box (channel) with…

INTRODUCTION: In this project, we will be simulating a `60^0` sector geometry for a CAT-3410 diesel engine with different piston profiles. The geometries are generated using the "make engine sector surface" tool available in CONVERGE Studio. The geometric parameters of the  1. Open-W Piston 2. Omega Piston The surface…