Computational Fluid Dynamics - Assignment Example

FV4003 CFD ASSIGNMENT Name: Institution: Date: Question 1: Mathematical Models (a) Equations Governing Fire Simulation There are three conservation equations governing the simulation of a fire in CFD. The three equations express the conservation of energy, mass and momentum. The equations, which are derived from the Navier-Stokes equations, are solved numerically using the most appropriate fire modelling software. These equations are suitably applied for low speed and thermally-driven flow, emphasizing on transport of heat and smoke from the fires (Wesseling, 2009). Mathematically, these governing equations are expressed in the form: Equations of conservation i. Conservation of Mass ii. Conservation of Energy: iii. Conservation of momentum: Where: – Density of fluid – Velocity of fluid – Temperature – Fire –induced pressure – Denotes the unresolved viscous stress tensors and momentum flux lumped together – Fluid vorticity – Vertical component of the velocity – Specific heat – Denotes radiant energy flux and conduction heat flux – Chemical heat released per unit volume – Ambient pressure – Height – Gravitational force Another important equation is the equation of State. This is an additional equation for a perfect gas used to obtain equations that relate relevant unknown variables. The equation is expressed in the form: Where: – Pressure – Density – Gas costant – Temperature – Volume of the fluid To solve the above governing equations, we need properly defined boundary conditions, or else, they will affect our solutions. Three types of boundary conditions in CFD include: physical boundary conditions, pressure conditions, and axisymmetric and symmetric boundary conditions. (b) CFD Modelling Reasons why CFD codes are written in low-speed solver and high-speed solver i. To be able to operate and solve a broad range of flow conditions. ii. To provide for a variety of boundary options, such as pressure inlet and outlet, velocity inlet and outlet, etc. A student cannot obtain acceptable results when simulating an object flying at 400m/s using FDS6. This is because the simulation model is designed for low- fluid speeds that are thermally driven. An object flying at such a high speed will simulate faster than the model can respond. (c) Pressure used in FDS Background hydrostatic pressure used in FDS = 2.4 Pa Different rooms can have different background pressures. This is because the regions in the rooms are separated by solid obstructions. Thus, the two rooms have different computational domains, unless the obstructions are identified and defined within the algorithm of FDS. Defining pressure zones using FDS input: Consider a rectangular region with dimensions and in a closed compartment. To identify these zones explicitly, we have the following input to the FDS. ZONE XB=0.4, 1.3, 0.5, 3.0, 0.4, 4.4 / The dimensions of the compartment are defined as: 0.4 Read More