Fluid Dynamics of Fires - Assignment Example

Fluid Dynamics of Fires Name Institutional Affiliation Date 1. Classical Mechanics of Fluids 1.1. According to Navier-Stokes equations below, some terms require turbulence modelling. Equation: Where; - Density - Time - Component of the total stress sensor - Body forces - Del operator The terms from the equation that require modelling include the deviator stress sensor with the dynamic viscosity denoted by and which relies on the temperature and pressure where temperature T is given by: 1.2. The relationship between the pressure drop and the head loss can be illustrated as shown in the formula shown below: From the formula above, stands for pressure at point 1, stands for pressure at point 2, stands for density of water whereas represents change in height. Thus, = 8.2m since the orifice has a connection made at the bottom of the tank. Thus, 2. Dimensional analysis 2.1. Finding dimensions The non-dimensional term from the above is From the above, is the non dimensional term 2.2. In dimensional analysis, the units for all the quantities are determined and just like numbers, divided and multiplied systematically or even cancelled out (Worstell 2014). From the problem description, the units for is m/s, kinematic viscosity (v) units are m2/s, units for density are kg/m3 whereas units for specific dissipation rate ( ) are J/(kg s). The overall relationship for these units assuming K is a constant. After solving the whole problem, the result for Right hand side and Left Hand Side are: Left Hand Side (LHS) = and RHS = Including the constant produces the relationship below Thus, the dimensions results do not yield equal dimensions, thus no relationship can be drawn out of the equation. 3. Heat Transfer, Thermochemistry, and Fluid Dynamics of Combustion 3.1. For PMMA, the RMM is given: Thus, 1 mole of PMMA is equal to 100 g For an amount of 1 Kg of fuel, the heat dissipation rate is 24.9 MJ/Kg And therefore, in 2.5 Kg of fuel, heat dissipated is equal to 3.2. How fast or slow a given reaction occurs is what defines a reaction rate. The reaction rate is affect by factors such as: Concentration of the active ingredients When the concentration of the active ingredients increases, the rate of reaction also increases and decreases with decrease in the concentration of the active ingredients (Venn 2013). In other words, the frequency of collision of the molecules increases with increased concentration . Temperature Temperature is cited to bring more energy that is necessary for the reaction in any given system. Therefore, the higher the temperature, the higher the rate of reaction. Order Both pressure and concentration of the reaction are affected by the sequence of the reaction, which in turn affect the reaction rate. Existing natural or environmental conditions Depending on the nature of the available environmental conditions, some reactions are naturally faster or slower than others are, and can depend on the reaction’s complexity. An example of a chemical reaction for burning of a gaseous fuel is: 4.0. Characteristics of Flames & Fire Plumes 4.1. Characteristics of a fire plume According to Madrzykowski (2013), there are quite a number of properties that determine generation of a fire plume in a compartment. They include; the position of a fire ,condition of the ambient in the compartment, amount of fuel, ventilation of the compartment (both natural and mechanical),geometry of the compartment and the fuel itself . These properties are determinant features in classification of the various stages in combustion of fire. a. Fire Ignition Stage This is the preliminary stage in combustion. Combustion at this level is initiated by fuel and thus marks the start of fires within the compartment. b. The Fire Growth stage As the title of the stage hints, fire at this stage develops further from the initial ignition. Fire grows as a result of the presence of the fire and not just the features of the given compartment. Given the presence of oxygen, the fire increases and grows to the entire compartment or building since oxygen aids the combustion process. Description of fire at this stage can be analysed in reference to the combustion and energy rates (Society Of Fire Protection Engineers 1998). c. Flashover Stage At this stage, the fire transits from growing to actually full development in the entire building or compartment. Other combustible elements in addition to oxygen come in at this stage. The hot gases in the compartment change their radiation and when they are involved in combustion with other items in the compartment, the fire explodes and becomes enormous. The part of the compartment used in the construction of the compartment becomes important sources of fuel. The temperatures at the beginning of the flashover stage are between 3000C to 6000C (Cox & Langford 2012). d. Fully Developed Fire At this stage the amount of heat released is at its greatest intensity. More and more fuel gets pyrolised than the oxygen present within the compartment. The only thing that can control the fire at this stage is the compartment’s ventilation. e. Decay Stage The items in the compartment have been overused and thus the intensity of the fire begins to decline. The rate at which the fire burns begins to slow down. Therefore, the amount of fuel in the fire and not necessarily the ventilation of the compartment control the fire in the compartment. This concept is illustrated in the figure below. Figure 1: Illustration of stages in fire development 4.2 Fire Growth and Compartment Ventilation In a reduced compartment, the position of the ventilation determines the rate at which fire grows and how it develops in the compartment. A series of experiments was conducted to investigate the influence of the ventilation and wind on smaller compartments. In this experiment, the compartment’s ventilation was adjusted to various positions. The velocity of the wind too was pegged at varying velocities. The experiment revealed that in smaller compartments with two or more openings, the growth of the fire was higher. The reason given was that oxygen available in the smaller compartments supported combustion. In addition to this, the ventilations allow smoke to get out of the compartment thus facilitating exchange of smoke and air in and out of the compartment. Given that that the walls in the smaller compartments are near the sources of fire, this factor that is prone to accelerate the growth of the fire. This gives another reason why smaller compartment would burn faster than larger compartments. Also important to note is that as the wall burns, the fire expands to other areas of the compartments. In the study too, it was noted that the flames were investigated and it was found out that they followed the ventilation References Top of Form Bottom of Form Top of Form Top of Form Top of Form Top of Form Bottom of Form Bottom of Form Bottom of Form Bottom of Form Cox, G., & Langford, B. 2012. Fire Safety Science. Hoboken, Taylor and Francis. http://public.eblib.com/choice/publicfullrecord.aspx?p=995627. Madrzykowski, D. 2013. Fire dynamics: the science of fire fighting. International Fire Service Journal of Leadership & Management. Society Of Fire Protection Engineers. (1998). Fire protection engineering. Bethesda, MD, Society of Fire Protection Engineers. http://www.sfpe.org/sfpe/fpemag.htm. Venn, C. C. (2013). Fire Dynamics. 959-997. Worstell, J. (2014). Dimensional analysis. http://site.ebrary.com/id/10847886. Read More