Analysis of Thermal Explosion in a Vessel with Cold Walls - Assignment Example

T1. Analysis of thermal explosion in a vessel with cold walls, including the mechanism of self-accelerating reaction and the nature of induction period? The mechanism of thermal explosion in a vessel with cold walls, including the self-acceleration and induction period can be explained through the thermal explosion theory. Basically, thermal explosion means the “sudden inflammation of a uniformly heated mass” of substance (Zukas Walters and Walters 176). It is further defined as the rapid heat release that is associated with self-acceleration, and often manifested through its destructive outcomes (Griffiths and Barnard 3; Glassman and Yetter 261). The analysis of thermal explosion is concerned mainly with the rate of heat generation of the exothermic reaction and the rate of heat dissipation to the surrounding. Before the explosion, the substance inside the vessel would be characterised by an induction period where the rate of exothermic decomposition reaction is slow. The produced heat would however be transferred through the walls of the vessels to allow heat balance in the system as determined by the Newton law. The rate at which heat is lost through heat transfer methods (such as conduction, convection, and radiation) is higher than the rate of heat production, especially because of the high temperature gradients; that is, heat would be transferred towards the cold walls of the vessel or rather the surrounding. This would cause the vessel wall to heat up to a temperature equal to the outside. In time, this temperature gradient between the vessel wall and the explosive substance would reduce as heat from the reaction of the substance is transferred to the walls of the vessel. It is worth to note that the vessel takes up heat as long the temperature outside is higher than that of the vessel; otherwise, the heat would be transformed to the outside. Often, it is assumed that the temperature of the vessel wall remains constant as long as it is being transformed into the outside (Kotoyori 4; Terao 4). In the meantime, the exothermic reaction would continue to produce more heat causing rise in temperature of the substance as well as increase in the rate of reaction. As long as the rate of heat production is lower that the rate of heat dissipation the system remains stable and no explosion is experienced. However, the self-acceleration of the exothermic reaction continues to a point where the rate at which heat is produced within the substance exceeds the rate at which heat is lost. Consequently, there is increased temperature build up to a point where it is critical to cause ignition of the substance. Thus, a thermal explosion occurs. T2. Explanation of the effect of heat transfer on thermal heat balance in a vessel with cold walls, critical conditions of thermal explosion, and pre-explosion heating using Semenov diagrams. Figure 1: Semenov diagram The rate of heat release by the reaction in the vessel fluctuates as “an exponential function of temperature”, while the heat transfer (heat loss) through the heat removal (cooling) system “varies linearly with temperature” (Stoessel 50). Thus, the exponential curves Q represent the rate of heat production by the reaction, while the broken lines curves, Q1, Q2 and Q3 represents the rate of cooling (heat loss). The intersections, A and B, of curve Q and curve Q1 show a state where heat balance is at equilibrium such that the rate of heat production is equal to the rate of heat loss. At intersection A, the equilibrium is stable. When the temperatures are below point A, there is more heat production until a state of equilibrium is reached. Inversely, deviation of the temperature to a higher value results in more heat removal until heat production and heat removal becomes equal. The intersection at B represents an unstable equilibrium. Lowering the temperature would result in more cooling towards the temperature at point A. However, an increase in temperature causes a thermal explosion. The intersection of line Q2 and curve Q represent an unstable condition, and the temperature of the cooling system at this point is known as critical temperature. The line Q3 represents a situation where there is no solution to the heat balance and always there is an explosion. T3. Definitions of explosion, deflagration and detonation, and explanation of the development and main features of detonation. Explosion can be defined as the sudden, rapid release of heat in an exothermic reaction (or sudden rise in pressure) that is associated with self-acceleration, and often manifested physically through its destructive outcomes (Griffiths and Barnard 3; Glassman and Yetter 261). However, deflagration is the rapid heat release associated with a subsonic wave of combustion that often propagates by thermal conductivity. Detonation is the rapid heat release of a chemical reaction that results in a supersonic wave that often propagates by shock compression. The development of a detonation starts with rapid heat release of a chemical reaction which results in a supersonic wave that propagates through the medium. Often, a confinement, explosive medium and an ignition source are the prerequisite conditions for a detonation. The main features of a detonation are that it has a supersonic wave and the propagation of this wave is by shock compression. T4. Review the main features of diffusion combustion, and explanation of the types of diffusion flames (momentum and buoyancy dominated fires) as well as comparison of the Froude number for these types of fire. Diffusion combustion is often characterised by a yellow flame with a spherical front. The combination of the fuel and the oxidizer occurs by diffusion. Thus, the rate of burning (also the rate of fuel consumption) is influenced by the rate of mixing of the oxidizer and fuel to an appropriate proportion for the reaction. Often, diffusion combustion results in more soot and slower flame burning as compared to premixed flames combustion due to insufficient oxidization. The combustion also produces incandescent soot that renders the flames to have a yellow-orange like colour. In addition, diffusion flames often have less localized front when compared to premixed flames. The two types of turbulent diffusion flames are momentum dominated flames and buoyancy dominated flames. The momentum dominated flame is associated with a high speed jet flowing from an opening, while a buoyancy dominated flame can be epitomized by a lethargic flame over a burning bowl of flammable liquid where its upward flow is propelled by buoyancy (Friedman 185). Momentum dominated flames have flame height that is proportional to the orifice’s diameter, and does not depended on the rate of flow. Conversely, the flame height of the buoyancy dominated flame correlates to the rate of convective heat release of the flame. It is also worth to note that the Froude number of a momentum dominated flame is higher than that of buoyancy dominated flame (Karlsson and Quintiere 51). T5. Analyse the burning rate of solids and mechanism of flame spread over solid surfaces. Burning rate refers to the rate at which a fire consumes a specific material. It can be represented in terms of rate of heat release. The burning rate of solids is determined by the nature of the material given that there is adequate oxygen (the oxidizer) (Tran and White 1). The nature of the solid material include factors such as the ratio of the surface area to the mass of solid, orientation such as vertical or horizontal, geometry and arrangement. The mechanism of flame spread in solid is understood. The flame at the source produces heat energy that raises the temperatures of the adjacent areas of the solid through the heat transfer methods to a point that ignition occurs. A number of factors determine the rate of flame spread. They include direction, radiative preheating, and thickness of the solid. Flame spread in an upward direction is faster than downward or horizontal spread. Preheating accelerates the rate of flame spread. The rate of flame spread over solids is inversely proportional to the solid’s thickness. T6. Analysis of emissivity of opaque surface and grey body, and determine the total black body emissive power and total grey body emissive power at a given temperature. The emissivity of a material is the ratio of energy emitted by a specific material to the energy emitted by a blackbody at same temperature. It is a measure of the ability of a material to radiate energy. This property depends on wavelength, emission angle, and temperature. The emissivity of an opaque surface is theoretically given as 1, although the laboratory emissivity value is given as 0.99 (Lipták 642). This is because an opaque surface absorbs virtually all electromagnetic radiation energy, and emits the maximum amount of radiation energy. For a grey body, the emissivity is less than 0.99. A black body total emissive power (E) is proportional to the fourth power of its thermodynamic (absolute) temperature (Zalosh 337). Thus, E = σT4 where σ is a constant = 5.67 x 10-8 W/m²K4 Therefore, at a temperature of 100K the emissive power of a black body is, E = 5.67 x 10-8 W/m²K4 * 1008 = 5.67 W/m² For a grey body, the emissive power (E) is given by, E = εσT4 where ε is the emissivity of the grey body. Therefore, the total emissive power of a grey body at 100K temperature is less than 5.67 x 10-8 W/m²K4 since emissivity is less than 1. T7. Analysis of the radiating gases produced in combustion, define the mean beam length and explain the use of emissivity charts. The radiating gases produced in combustion include water and carbon dioxide. The gases are characterised by “a homogenous mixture” (Baukal and Schwartz 106). One part of the mixture is capable of radiation, while another part is not. The emissivity of these gases is very low (Baukal and Schwartz 106). The amount of heat radiated from these gases is relatively a small part of the entire heat energy of the gases. The definition of the mean beam length refers to the calculations of heat transfer where an isothermal, emitting-absorbing medium is contained within a black-walled isothermal enclosure; note that the medium does not scatter). Therefore, the mean beam length is a directional average of the medium’s thickness of the “as seen from the point on the surface” (Bejan and Kraus 623). Emissivity charts are useful in readily providing emissivity values for various materials, and avoiding the cumbersome process of computing the values for every material (Modest 340). T8. Critical analysis of the effect of ventilation on the composition of smoke using equivalence ratio, and comparison of over ventilated and under ventilated combustion. Ventilation plays a critical role in the composition of smoke. It refers to process in which air (oxygen) is provided to as space while stale air is eliminated. In this case, it refers to the availability of air in combustion process. Thus, ventilation is important in combustion because it determines the amount of the oxidizing agent (oxygen) available for combustion. Using equivalence ratio, the ratio of the fuel-to-oxidizer ratio to the stoichiometric fuel-to-oxidizer ratio, it is possible to determine whether the correct amounts of fuel and oxidizer needed in a mixture for complete combustion to take place. Thus, an equivalence ratio that is above one show that the fuel/oxidizer mixture has excess fuel, while a ratio that is below one show excess oxidizer (fuel deficiency) in the mixture (Basu 86). Accordingly, an equivalence ratio that is greater than one show inadequate ventilation, while adequate ventilation is represented by a lower ratio. Therefore, complete combustion would occur when the equivalence ratio is one or below because in such a case the fuel is completely burn. In a complete combustion involving a hydrocarbon and oxygen as the oxidizer, the resultant products would be water and carbon dioxide. However, with an equivalence ratio greater than one, incomplete combustion would occur and result in additional products such as soot and carbon monoxide. These products are what constitute the smoke. Therefore, smoke concentration increases with increasing equivalence ratio. It also worth to note that complete combustion is associated with high temperatures and this could contribute to aerosols and vapours in the smoke. Over ventilated combustion have an equivalence ratio that is less than one; that is, there is excess air (oxygen) than the amount required for complete combustion. On the other hand, under ventilated combustion have equivalence ratio that is greater than one; meaning that air (oxygen) available is less than what is required for complete combustion. T9. Analysis of smoke optical properties: absorption, scattering and extinction of light, including examination of the role of extensive (extinction coefficient, optical density per meter, optical density per meter) and specific characteristics (mass extinction coefficient, mass optical density per meter, smoke potential) and their relationships. Smoke has the ability to absorb, scatter, and extinct light rays. Smoke consists of particles that are responsible for absorption of light energy and scattering of lights rays. Both absorption and scattering by smoke eliminate energy from the light rays passing through it; in other word, a beam of light is attenuated. This is what is known as extinction (Hulst and van de Hulst 3). These optical properties are dependent on factors such as extinction coefficient and optical density per meter. The extinction coefficient of smoke shows various measures of light absorption in a medium. Thus, mass extinction coefficient indicates the ability of smoke to absorb light at specific wavelength for each unit mass, while molar extinction coefficient indicates the ability of smoke to absorb light at specific wavelength for each molar concentration. A high extinction coefficient would indicate that the smoke has a high capability of absorbing light energy and causing extinction, and vice versa. The optical density of smoke is its absorbance for specific wavelength per unit meter. It is useful as a measure of transmission of a medium for a particular wavelength, or rather the amount of light obscured (Patterson 24), in this case, by smoke. Thus, higher optical density indicates lower transmittance of light energy by smoke and vice versa. Smoke potential is dependent on these factors and indicates the capability of smoke to absorb, scatter, and cause extinction of light energy. T10. The main sources of heat release and heat loss in a typical compartment fire. Analysis of the difference between burning rates in open space and in a compartment. The main sources of heat release in a typical compartment fire would be the combustion of fuel materials within the compartment, while heat loss sources could include heat transfer through various medium by radiation, conduction and convention methods. Ventilation or rather circulation of air plays an important role in heat loss. However, it is worth to note that ventilation would provide air to allow complete combustion, and hence more heat is release. The burning rates can differ for combustion occurring at open space with those occurring in a compartment. For instance, compartment fires often rapidly consume the available oxygen in a compartment such that there is little oxidizer to support combustion. This slows down the rate of burning. Conversely, fires in open space burn much higher rates due to the availability of oxygen (air). Note that this consideration is when other factors such as the nature of material burning are the same. References Basu, Prabir. Combustion and gasification in fluidized beds. CRC Press, 2006. Baukal, Charles E. and Schwartz, Robert E. The John Zink combustion handbook. CRC Press, 2001. Bejan, Adrian and Kraus, Allan D. Heat transfer handbook, Vol. 1. Wiley-IEEE, 2003. Friedman, Raymond . Principles of Fire Protection Chemistry and Physics. Jones & Bartlett Learning, 2008. Glassman, Irvin and Yetter, Richard A. Combustion. Academic Press, 2008. Griffiths, J. F. and Barnard, J. A. Flame and combustion, 3rd edn. CRC Press, 1995. Hulst, Hendrik C. and van de Hulst, H. C. Light scattering by small particles. Courier Dover Publications, 1981 Karlsson, Björn and Quintiere, James G. Enclosure fire dynamics. CRC Press, 2000. Kotoyori, Takashi. Critical temperatures for the thermal explosion of chemicals. Gulf Professional Publishing, 2005. Lipták, Béla G. Instrument Engineers' Handbook: Process measurement and analysis. CRC Press, 2003. Modest, Michael F. Radiative heat transfer. Academic Press, 2003. Patterson, James. Simplified design for building fire safety. Wiley-IEEE, 1993. Stoessel, Francis . Thermal safety of chemical processes: risk assessment and process design. Wiley-VCH, 2008. Terao, Kunio. Irreversible phenomena: ignitions, combustion, and detonation waves, Springer, 2007. Tran, Hao C. and White, Robert H. Burning rate of solid wood measured in a heat release rate calorimeter. Fire and Materials, Vol. 16, pp. 197-206. 1992. Zalosh, Robert G. Industrial fire protection engineering. John Wiley and Sons, 2003. Zukas, Jonas A., Walters, William and Walters, William P. Explosive Effects and Applications. Springer, 2002. Read More