Fluid Dynamics of Fires - Assignment Example

FV2001 Assignment Brief Assignment Details 1. Classical Mechanics of Fluids (25 marks) 1.1. The Navier-Stokes equations govern fluid flow in fires and fire protection systems. It is the foundation for water flows, gas flows, and fire simulations and modelling. Please list the Navier-Stokes equations together .Twith the equations of energy conservation. Explain the physical meanings of each term in the momentum conservation equations. Indicate what terms in the equation need turbulence modelling and give the reasons why turbulence models are necessary? Give an example of the source term in the equation of energy conservation. Answer Navier-Stokes equations -Fluid density - time - Component of the total stress sensor - Body forces - del operator What terms in the equation need turbulence modelling The deviatoric stress sensor has the dynamic viscosity and which depends on pressure and temperature [15 marks] 1.2. A pressure meter is calibrated using a Venturi meter attached to a small orifice at the bottom of a water tank. The cross-section areas of the wide and narrow parts of the Venturi meter are of 6 cm2 and 2 cm2 correspondingly. What should be the pressure drop between the wide and narrow parts of the Venturi meter, when the water level in the tank is 8.2 m? Please assume the Venturi meter is installed with pipes of cross-sectional area of 6 cm2 and the pipe finally discharges to open air at the outlet. Answer Pressure drop and head loss are related as shown in the formula below. Where = pressure at point 1 = pressure at point 2 = density of water =change in height Since the orifice is connected at the bottom of the tank, =8.2m 2. Dimensional analysis (25 marks) 2.1. Find the dimensions of the following terms. What term(s) are/is non-dimensional? [12 marks] 2.2. Kolmogorov scale of velocity in homogeneous turbulence depends on the kinematic viscosity coefficient v [m2/s], specific dissipation rate [J/(kg s)] and, maybe, of fluid density [kg/m3]. Obtain the formula for this dependence using the dimensional analysis. [13 marks] 3. Heat Transfer, Thermochemistry and Fluid Dynamics of Combustion (25 marks) 3.1. Burning of polymethylmethacrylate (PMMA) can be described by the following chemical reaction formula. Explain the process of the burning of the PMMA (pyrolysis and reaction with oxygen) and calculate the stoichiometric fuel-air ratio. If 2.5kg of PMM is burnt, how much heat is produced? Answer Relative molecular mass (RMM) for PMMA = (12*5)+(1*8)+(16*2)=100, One mole of PMMA=100g, The rate of heat dissipation is i.e. for 1kg of fuel Therefore 2.5kg of fuel= 2.5*24.9=62.25MJ/kg 3.2. Define the Reaction Rate of a fire, then, discuss the factors that affect the reaction rate in a general secondary-order A + B → C + D chemical reaction. Give an example of such a chemical reaction of burning a gaseous fuel. [10 marks] Answer, Reaction rate of fire refers to how fast or how slow a reaction takes place. Factors that affect the reaction rate Nature of reaction, depending on the fuel type and the existing environmental conditions, some reactions are naturally slower or faster than others. This is also affected by the complexity of the reaction. Concentration- it is well understood that the rate of reaction increases with the concentration of active ingredients within the fire. This explained by the collision theory, of the rate law, where, frequency of collision increases as concentration increases. Order- The sequence of the reaction regulates the concentration and pressure of the reaction, thereby affecting reaction rate. Temperature-generally a higher temperature during reaction, brings in more energy within the system Example of gaseous combustion is the burning of methane in oxygen 4. Characteristics of Flames & Fire Plumes (25 marks) 4.1. Fire plumes are important in fire dynamics. Using a solid fuel fire at the centre of a compartment as an example, explain the characteristics of a fire plume and generalise the axisymmetric plume model for calculating the smoke production rate and temperature along the axis of the fire plume. [15 marks] Answer Characteristics of a fire plume The development of fire plume in a compartment is influenced by many properties including the proportion the fuel, quantity of fuel, natural and mechanical ventilation, the geometry of the compartment, location of the fire and ambient condition in the compartment. Therefore, the combustion of fire in the compartment can be divided into the following stages of development. a. Fire Ignition Stage This is the initial stages in combustion which is initiated by the combustion of fuel. Hence it is the beginning of fires in the compartment. b. The Fire Growth stage This is the stage in which the fire in the compartment grows as a function of fuel and has little influence from the features of the compartment. This means that the fire in the growth stage can be described in terms of the rate of energy and combustion energy. In the presence of oxygen, the growth of fire will continue and spread to other areas of the compartment and building. This is because oxygen supports combustion and keeps the fire growing. c. Flashover Stage This is the transition stage from fire growing stage to full fire development in the compartment. During this stage, the combustible items in the compartment are also involved in the compartment fire. This means that all the available flammable materials used in the construction of the compartment acts sources of fuels in the flashover stage of fire development. This stage involves the ignition of combustible items in the compartment in which there is a change in radiation from the hot gases in the compartment. The onset of flashover stage is characterised by temperatures of between 3000C to 6000C. However, temperatures of 500-600 degrees Celsius are mostly used. d. Fully Developed Fire At this stage, the amount of heat released from the combustible items in the compartment is at its greatest. During this stage, more fuel is pyrolized than with the oxygen that is present in the compartment. This means that the fire is controlled by the ventilation of the compartment. e. Decay Stage As the fuel used in the combustion of compartment items become used, the rate of fire also slows down. This means that the rate of heat produced in the fire is also declining. This implies that the fire in the compartment is no longer controlled by the ventilation of the compartment but controlled by the fuel used in the fire. This is illustrated in the figure below. 4.2 Diffusion flames are common in compartment fires. Assuming a solid fuel is ignited, discuss and analyse factors that affect the spread of the flame on the solid fuel surface. If the fuel is a gas or a liquid, how the flame will spread? [10 marks] Fire Growth and Compartment Ventilation The location of ventilation in a reduced compartment is crucial in determining the fire growth rate and flashover process in fire development. In order to establish the effects of wind and ventilation on smaller compartment, conducted a series of experiment using different scenarios in which the ventilation were placed at a different location in a model compartment. In this experiment, the wind velocity was set at various velocities. The growth of fire is high in smaller compartments that have more than two openings. This is because there is available oxygen, which supports the burning of the fire. In addition, a well-ventilated compartment allows the smoke to escape from the compartment hence ensuring an exchange of air with smoke with the outside environment. In smaller compartments, the walls of the compartment are in proximity to the sources of fire. This means that the walls of the smaller compartment burn faster and easily. As the walls burn, the fire spreads to other location of the compartment. The behaviour of the flames was also investigated such that flames were observed to follow the ventilation. The transfer of heat in compartment walls can be expressed using the equation q = Conducted thermal energy (kW). k = Coefficient of thermal conductivity. A = Area of surface in question (m2). T = Absolute temperature of surface in question (K). x = Thickness of material in question (m). Read More