Fluid Dynamics of Fire - Research Paper Example

FLUID DYNAMICS OF FIRE Student’s Names Institutional Affiliation Date Fluid Dynamics of Fire 1.0 Classical Mechanics of Fluids 1.1 The Navier-Stokes equations comprise of the equation of continuity, the momentum equation, and the energy equation (NASA, 2013). Continuity: Momentum: x-momentum: y-momentum: z-momentum: Energy: +] Where (x, y, z) =coordinates, t=time, p=pressure, ρ=density, , (u, v, w)=velocity components, q=heat flux, Re=Reynolds number, Pr=Prandtl number The equations of energy conservation include the Bernoulli equation and the first law of thermodynamics equations The Bernoulli equation The Bernoulli equation for conservation of energy can be written as (University of Leeds, 2010) Where The momentum conservation equations Conservation of momentum is embodied in the Newton’s First Law-Law of inertia. For one-dimentional steady flow, the equations is Where, The general equation that caters for all the coordinates is Where j is the coordinates. All terms with Reynolds Number and Prandtl Number in the Navier-Stokes equations needs turbulence modelling. Turbulence modelling is important in fluid dynamics because it helps in predicting the effect of turbulence in the fluid system. The source term in the energy conservation equation is the total head (H). The total head can be the total energy within a water system, for example, water flowing from a reservoir. 1.2. The pressure in the wider part of the pipe before the contriction is the same pressure exerted by the water in the tank. Let the wider part of the pipe be point 1 and, the narrow part be point 2. Therefore, A1=6 cm2 and A2=2 cm2 The mass flow rate is the same at point 1 and point 2 indicated by the continuinity equation (Engineers Edge, 2014) Where From the equation, From a simplified Bernoulli principle, Simplification of the two equations results in Therefore, the pressure drop between point 1 and point 2 is 333.33 times the square of the velocity of water passing at point 2. 2. Dimensional analysis 2.1. Find the dimensions of the following terms. What term(s) are/is non-dimensional? [12 marks] The letters L=length (m), M=mass (kg), T=time (s) a) b) c) d) e) None of the terms above are dimensionless. 2.2. Using dimensional analysis to derive formula for the dependence of the Kolmogorov scale of velocity . Density has also been included in the calculation for the dependency of the Kolmogorov scale . Sorting terms with similar bases give Hence, the final formula is 3. Heat Transfer, Thermochemistry and Fluid Dynamics of Combustion 3.1 PMMA can be burnt both in the presence and absence of oxygen. In the absence of oxygen (pyrolysis), the polymer is burned under pressure and controlled temperature. Lower temperatures produce charred-solid while higher temperatures may liquidify the material. However, when heat is applied to PMMA in presence of oxygen, it begins to decompose due to heat energy. Thermal decomposition of PMMA is accompanied by both the physical and chemical phases’ changes, which are irreversible. The stoichiometric fuel-air ratio Atomic weights C=12 H=1 O=16 Molecular weight of oxygen =16*2=32 Molecular weight of PMMA=12*5+1*8+16*2=100 Therefore, the fuel-oxygen ratio=100/(6*32)=100/192=0.521. 0.521 kg of fuel requires 1kg of oxygen to burn. Since around 23.2 mass percent of air is oxygen, 1kg*100/23.2=4.310kg of air would be required to provide the 1kg oxygen for combustion. Thus, 0.521kg of fuel needs 4.310 kg of air. It gives a fuel-air ratio of 0.521/4.310=0.121 Heat produced The reaction produces heat at the rate of 24.9MJ/kg. As a result, 2.5kg of PMMA would produce 2.5*24.9=62.25MJ/kg 3.2. The reaction rate of fire is the speed at which the fuel combusts in the presence of oxygen. In addition to oxygen, the reaction rate of fire depends on the subsequent heat released by the exothermic reaction of fire. Factors that affect the reaction rate of a chemical reaction Factors that affect chemical reaction (general secondary-order) include the concentration of the reactants, pressure, temperature, nature of the reactants, and the presence or absence of catalysts (Centre for Distance Learning and Innovation-CDLI, 2014). Concentration of reactants The rate of a chemical reaction increases with the concentration of the reactants and reduces as the reactants are depleted. Pressure of the reactants Pressure affects the rate of a chemical reaction, especially where gaseous reactants are involved. The reaction would increase with pressure and falls as the pressure reduces. As the pressure increases, the number of molecules in a particular volume is compressed and, as a result, the molecules react faster. Temperature Most chemical reactions are faster at a higher temperature and diminishes as the temperature reduces. As the temperature increases, the kinetic energy of reactants molecules also increases, which enhances the chemical reaction rate. Nature of the reactants Individual properties of reactants affect the rate of the rate of a chemical reaction. The state of matter, bond strength, and bond size are some of the individual properties of reactants that influence the rate of a chemical reaction (CDLI, 2014).. For instance, gases react faster than liquid or solids. Reactants of ionic species react faster than molecular species. The presence or absence of a catalyst A catalyst would increase the rate of chemical reactions while some reactions may not proceed without a catalyst. Example of a secondary chemical reaction of burning a gaseous fuel The combustion of methane gas to produce heat, carbon dioxide, and water. CH4 (g) + 2 O2 (g)   →   CO2 (g) + 2 H2O (l) 4.0 Characteristics of Flames & Fire Plumes 4.1. Characteristics of a fire plume When a solid fuel or material is heated, it starts to emit gases before mixing with the oxygen (diffusion fire). The fuel is pyrolysized before bursting into flame when its gases mix with oxygen. The gases released as the solid fuel smoulders partially burn in the flame, and the unburned gases accompany the fire flume held in the smoke gas layer. A plume develops as a diffusion flame spread on the solid fuel. As the flame is formed, a flow of hot gas is formed above in and above it. The heat released by the fire determines the properties of the fire. The higher the heat release rate, the faster the smoke and heat spread within the compartment. The temperature gradient along the hot gaseous mass also results in a difference in density. The hot part of the gases in the plume, which has a low density rise upwards while the highly dense and low temperature part of the gases remains at the bottom part of the plume. A fire plume is divided into three zones, namely continuous flame zone, intermittent flame zone, and far field zone (Bandi, 2010). The continuous flame zone has a flame of a continuous velocity. The intermittent flame is the section of the fire with a fluctuating flame while the far field zone is characterised by decreasing gas velocity and temperature with height (Bandi, 2010; Bengtsson, 2011). The gas velocity and temperature of the fire plume depends on the heat released from the fire and the height above the fire (Bengtsson, 2011). The mass influx increases in the plume as the air mix with the gases. As the vertical height increases, the temperature and velocity of the gases decrease. A generalised axisymmetric plume model The fire flow field is dominated by a thermally induced buoyancy that controls the compartment flow field (Heatkit, 2013).. The axis of symmetry exists along the centreline of the plume. Both the plume velocity and temperature are maximum at the centreline and decreases towards the edges. The velocity at the centreline increases in the continuous flame zone while decreases in the intermittent zone as more air is absorbed in the plume. The temperature at the centreline is almost constant in the continuous flame zone while decreases with height above the flame as ambient air cool the plume. The mass flow rate of the plume is upward and increases steadily with height as more air is absorbed in the plume (Heatkit, 2013). 4.2 The rate at which the flame spread on a solid fuel surface depends on material’s thermal inertia, the surrounding environment, the surface’s geometry, and the surface direction (Bengtsson, 2011). Material’s Thermal inertia Material’s property affects how a fire spreads on its surface. Materials with larger thermal inertia experiences slower flame spread on their surfaces (Bengtsson, 2011). Thus, flame spread faster on the surface of smaller thermal inertia materials. Surface direction The flame normally spread faster in an upward direction. Therefore, solid fuel heats up faster upward than downwards. As a result, the vertical flame spread faster than the lower flames. The height of flames is longer in the upward gradient than on the lower ones (Bengtsson, 2011). Surface geometry Close interaction between burning surfaces enhances the rate of flame spread. The smaller the angle between surfaces, the faster the flame spread. The enclosed areas tend to trap heat that in turn heat up the material that spread the flame. The surrounding environment The condition of the surrounding environment of the material influence the spread of flame. The flame spread rate increases with the ambient temperature and reduces as the temperature falls. High temperature promotes sustained burning the ensure flame spread faster. Flame spread for a liquid or gas fuel Unlike in the case of the solid fuel, which spread mainly through conduction, the liquid or gaseous fuel spread through convection and radiation. In most cases, the flame spread is spontaneous as the fuel occupies the confined surface faster than solid materials. In addition, liquids and gases have low densities compared to solids, therefore, burn faster. Bibliography Bandi, A., 2010. Fire plumes and fire heights. Available at: < https://www10.informatik.uni-erlangen.de/Teaching/IGWA/2013/report/course1/pdfs/15_IITB_AB.pdf>[Accessed 14 March 2015] Bengtsson, L., 2011. Enclosure fires. Available at: [Accessed 16 March 2015] Centre for Distance Learning and Innovation, 2014. Collision theory, reaction mechanisms and catalysts: Factors affecting reaction rates. Available at: [Accessed 16 March 2015] Engineers edge, 2014. Application of Bernoulli's Equation to a Venturi . available at: [Accessed 16 March 2015] Heatkit, 2013. Compartment fires. Available at: < http://heatkit.com/research/Compartment%20Fires.pdf.>[Accessed 11 March 2015] National Aeronautics and Space Administration (NASA), 2013. Navier-Stocks equations. Available at: [Accessed 15 March 2015] University of Leeds, 2010. The Bernoulli equation. Available at: [Accessed 15 March 2015] Read More

CH4 (g) + 2 O2 (g)   →   CO2 (g) + 2 H2O (l) 4.0 Characteristics of Flames & Fire Plumes 4.1. Characteristics of a fire plume When a solid fuel or material is heated, it starts to emit gases before mixing with the oxygen (diffusion fire). The fuel is pyrolysized before bursting into flame when its gases mix with oxygen. The gases released as the solid fuel smoulders partially burn in the flame, and the unburned gases accompany the fire flume held in the smoke gas layer. A plume develops as a diffusion flame spread on the solid fuel.

As the flame is formed, a flow of hot gas is formed above in and above it. The heat released by the fire determines the properties of the fire. The higher the heat release rate, the faster the smoke and heat spread within the compartment. The temperature gradient along the hot gaseous mass also results in a difference in density. The hot part of the gases in the plume, which has a low density rise upwards while the highly dense and low temperature part of the gases remains at the bottom part of the plume.

A fire plume is divided into three zones, namely continuous flame zone, intermittent flame zone, and far field zone (Bandi, 2010). The continuous flame zone has a flame of a continuous velocity. The intermittent flame is the section of the fire with a fluctuating flame while the far field zone is characterised by decreasing gas velocity and temperature with height (Bandi, 2010; Bengtsson, 2011). The gas velocity and temperature of the fire plume depends on the heat released from the fire and the height above the fire (Bengtsson, 2011).

The mass influx increases in the plume as the air mix with the gases. As the vertical height increases, the temperature and velocity of the gases decrease. A generalised axisymmetric plume model The fire flow field is dominated by a thermally induced buoyancy that controls the compartment flow field (Heatkit, 2013).. The axis of symmetry exists along the centreline of the plume. Both the plume velocity and temperature are maximum at the centreline and decreases towards the edges. The velocity at the centreline increases in the continuous flame zone while decreases in the intermittent zone as more air is absorbed in the plume.

The temperature at the centreline is almost constant in the continuous flame zone while decreases with height above the flame as ambient air cool the plume. The mass flow rate of the plume is upward and increases steadily with height as more air is absorbed in the plume (Heatkit, 2013). 4.2 The rate at which the flame spread on a solid fuel surface depends on material’s thermal inertia, the surrounding environment, the surface’s geometry, and the surface direction (Bengtsson, 2011). Material’s Thermal inertia Material’s property affects how a fire spreads on its surface.

Materials with larger thermal inertia experiences slower flame spread on their surfaces (Bengtsson, 2011). Thus, flame spread faster on the surface of smaller thermal inertia materials. Surface direction The flame normally spread faster in an upward direction. Therefore, solid fuel heats up faster upward than downwards. As a result, the vertical flame spread faster than the lower flames. The height of flames is longer in the upward gradient than on the lower ones (Bengtsson, 2011). Surface geometry Close interaction between burning surfaces enhances the rate of flame spread.

The smaller the angle between surfaces, the faster the flame spread. The enclosed areas tend to trap heat that in turn heat up the material that spread the flame. The surrounding environment The condition of the surrounding environment of the material influence the spread of flame. The flame spread rate increases with the ambient temperature and reduces as the temperature falls. High temperature promotes sustained burning the ensure flame spread faster. Flame spread for a liquid or gas fuel Unlike in the case of the solid fuel, which spread mainly through conduction, the liquid or gaseous fuel spread through convection and radiation.

Read More