Fluid Dynamics of Fire - Assignment Example

FV2001 ASSIGNMENT Name: Course: Professor: Institution: Date: 1. Classical Mechanics of Fluids 1.1. The Navier-Stokes equations describe the motion for a viscous fluid that is heat conducting, obtained by application of Newton’s second law of fluid motion. There are three fluid flow governing equations: the momentum equation, continuity equation, also called the mass conservation equation, and the energy equation. These equations can be expressed mathematically as shown below: i. = + F + u, (Equation of motion) ii. ) = 0, (Continuity equation) iii. + . u = 0, (Equation of energy conservation) iv. + .u u.u) + g, (Momentum equation) Where: u - The velocity of the viscous fluid - Thermodynamic energy - Fluid pressure - Temperature - Fluid density - Dynamic viscosity of the viscous fluid - Coefficient of heat conduction - External force acting on the fluid (per unit mass) - Gravitational acceleration (per unit mass) The two terms that require turbulence modelling are the fluid velocity vector and the pressure (Doering & Gibbon, 1995). The presence of turbulence in a fluid flow dominates over other flow phenomena, and makes it difficult to capture every single scale of fluid motion (Davidson, 2016). Successful turbulence modelling increases the quality of numerical CFD simulations by averaging all the unsteady fluctuations without capturing all the scales of vortices in a fluid flow. Capturing every scale of motion would require super computers because of the complexity involved. The velocity vector is an example of a source term in the energy conservation equation. 1.2 (b) P1 = P2 = P1 – P2 = ( ) (1.2 )P2 = ( ) P2 = ( ) (1.2 ) = 1000 9.8 (21 1) (1.2 ) = 1.004 Pa = 10.4 bar (c) Using Swamee-Jain equation, the friction factor can be calculated from: = Relative pipe roughness = = Assuming that the velocity through the riser is constant, Where: (1.2-1.004) = A1v1 = A2v2 v2 = A1v1/A2 Velocity in the hose (v2) = v2 = 30.94m/s Q = Av = ( RE = / Where: RE – Reynolds number – Velocity of flow – Dynamic viscosity RE = = > 4000 (turbulent flow) (Kiij¨arvi, 2011). = = 0.021 2.0 Dimensional analysis 2.1 = = kg/s = = = = s 2.2 The Kolmogorov scale of velocity depends on kinematic viscosity, specific dissipation and fluid density. Thus, = [L/T)= [L2/T] a [L2/T3] b [M/L3] c Comparing the dimensions on both sides; Comparing the dimensions on both sides, we have: For L 1=2a +2b -3c For T: -1 = -a-3b For M: 0 = c Therefore, c = 0, Solving for a&b, we have two simultaneous equations (i) and (ii) below: 1 = 2a + 2b ………. (i) 1 = a + 3b ………… (ii) Solving the equations, we have, a = b = ¼ So, the formula for Kolmogorov scale of velocity becomes: (Gibbings, 2011). 3.0 Heat Transfer, Thermochemistry and Fluid Dynamics of Combustion 3.1 The ignition and combustion of a wooden material is largely based on pyrolysis. This involves thermal decomposition of cellulose as well as reactions between pyrolysis products and air, mainly oxygen gas. As temperature rises, cellulose begins to pyrolyse. On thermal decomposition, the materials are either released as gases or remain in the wood material. Gaseous products react with each other in the presence of oxygen, producing greater amounts of heat that further increases combustion and pyrolysis reactions. Depending on conditions such as, oxygen concentration, temperature, fire retardants, moisture, pH etc. the process of pyrolysis can proceed in two main pathways; the tar-forming pathway and the char-forming pathway. The tar-forming pathway occurs at about 300oC and is largely related to the normal burning process of wood (Sinha, et al., 2005). On this pathway, pyrolysis process produces large amounts of tar, like the levoglucosan that easily decomposes under heat to form burning gases. In the process of thermal decomposition through char-forming process, cellulose is transformed into an unstable active cellulose that further undergoes decomposition to produce carbon dioxide, water and the cellulose backbone containing carbon. When a wood burns with a constant heat release rate per unit area, the pyrolysis front continues into the depth of the wood. All parolysing, wood material can be said to char at a rate corresponding to the rate of propagation of the pyrolysis front. Factors affecting the charring rate of wood include; the moisture content, external heat flux and the wood density. The charring rate of wood is an important quantity for the material’s fire resistance characteristics when used in structures, since original properties of a wood material are preserved under the char layer. A literature value of the charring rate of a wooden material ranges from 0.5 – 1 mm/min. Rising atoms of carbon and burning gases during combustion produces a light effect known as incandescence, which causes a visible flame. The color of the flame depends on what material is being burned and at what temperature. The variation in color within a flame is determined by the temperature at that region. Normally, the base of a flame is the hottest part and glows blue, while the lower temperature outer areas glow yellow or orange. Heat transfer is one of the most important factors in fires, and also has a significant effect on ignition, fire growth, spread, decay and extinction. It also plays a role in trying to establish the cause of fire. There are two main processes through which heat is transferred when wood is burnt are convection and radiation. Convectional heat transfer takes place when the heated gases from the burning wood transfer heat energy to cooler regions. The rate at which heat is transfer depends, among other factors, the temperature difference between the heat source and the cooler outer regions. Radiation is aided by electromagnetic waves that transfer heat energy from the burning wood to a cooler surface. The rate of heat transfer by radiation is dependent on the difference in the 4th power of the absolute temperature of the target and the source of radiation. When a wood material continues to burn, a pyrolysis front is formed on the wood. This forms a boundary layer between the intact wood and the pyrolysed material. The pyrolysing material is considered to char and as the char yield increases, a protective layer is formed. These protective layers may be effective in barring ignition and further charring of the wood material. 3.2 Reaction rate of fire is the rate at which a material is combusted into the products of combustion, such as water, carbon dioxide and carbon. The rate of fire reaction is determined by three main factors, also known as components of a fire triangle (Raymond Friedman, 2008). The first three factors that control the rate of combustion are components of the fire triangle. They are heat, oxygen and fuel. They are heat, fuel and oxygen. Other factors are presence of catalysts and the surface area and nature of the fuel. The general equation of reaction can be represented as: Fuel + Heat + Oxygen Combustion products High moisture content in a material reduces the rate of combustion. Woods with high content of resin will burn faster than those that do not contain resins. The nature of the fibers synthesized by a tree also affects the rate of combustion. Increasing the concentration of oxygen increases the combustion rate. A fuel with a larger surface area exposed burns faster than an intact fuel. Increasing the temperature raises the molecular kinetic energy of both the fuel and oxygen, thus, increasing collisions that increases the rate at which combustion takes place. The presence of chemical catalysts speeds up the rate of combustion reaction. Example of a chemical reaction when gasoline is combusted: C8H18 + + 12.5O2 8CO2 + 9H2O 4.0 Characteristics of Flames & Fire Plumes 4.1 Characteristics of fire plumes Plume velocity – This is the rate at which the plume moves form the fire source to the atmosphere. Plume rise - The plume rise is the mean vertical height at which a plume will rise most of the time. The height of a plume can be measured by comparing the mean plume height with a known height of an object. Plume mass – This is a property that measures the mass flow of a plume and can be calculated using the temperature of the plume and its temperature. However, plume turbulence and viscosity makes it a challenge to measure plume mass flow (Li & Chow, 2007). Plume turbulence – In unstable atmospheric conditions, a plume will undergo a transition stage, from laminar flow to turbulent flow as it rises. The instability between warm and cold air causes eddies that roll on the plume. Air entrainment – This is a plume property that determines the air content of a given plume, and affects the plume mass. A plume with a higher proportion of entrained air will be heavier than a plume with little air entrainment (Karlsson & Quintiere, 1999). The axisymmetric plume model is designed for a fire that is centrally located in a hall, with ambient air entrainment from all the sides of a plume and is based on the diffusion of plume. Along the vertical centerline of the plume where the temperature is maximum, a symmetrical line of axis is assumed. The temperature reduces away from the centerline towards the edges. 4.2 Factors that affect the spread of the flame on the solid fuel surface Availability of oxygen – Increasing the concentration of oxygen increases the rate of reaction between the fuel and oxygen, and this increases the spread of fire in a compartment. The size and the surface area exposure of the fuel – A fuel burns faster when more of its surface are is exposed to oxygen. The fuel load determines the rate of spread of fire. A larger size of fuel load will increase the rate of spread of fire (Takahash, et al., 2007). Density of the fuel – Heavier materials tent to conduct more heat compared to lighter materials of the same generic. The high density materials also allow more heat energy to stay longer at the surface, preventing the spread of fire. Light fuels ignite more rapidly and will favor a quick spread of fire. Moisture content of the fuel – Drier fuels will ignite and burn faster than fuels with higher moisture content. Thermal energy produced – Different fuels will produce different amounts of heat of combustion depending on the reaction conditions. Thus, a fuel with high heta of combustion produces more heat that can spread faster. References Read More

The charring rate of wood is an important quantity for the material’s fire resistance characteristics when used in structures since the original properties of wood material are preserved under the char layer. A literature value of the charring rate of a wooden material ranges from 0.5 – 1 mm/min.

Rising atoms of carbon and burning gases during combustion produces a light effect known as incandescence, which causes a visible flame. The color of the flame depends on what material is being burned and at what temperature. The variation in color within a flame is determined by the temperature at that region. Normally, the base of a flame is the hottest part and glows blue, while the lower temperature outer areas glow yellow or orange.

Heat transfer is one of the most important factors in fires, and also has a significant effect on ignition, fire growth, spread, decay, and extinction. It also plays a role in trying to establish the cause of the fire. There are two main processes through which heat is transferred when the wood is burnt are convection and radiation. Convectional heat transfer takes place when the heated gases from the burning wood transfer heat energy to cooler regions. The rate at which heat is transferred depends, among other factors, on the temperature difference between the heat source and the cooler outer regions. Radiation is aided by electromagnetic waves that transfer heat energy from the burning wood to a cooler surface. The rate of heat transfer by radiation is dependent on the difference in the 4th power of the absolute temperature of the target and the source of radiation.

When a wood material continues to burn, a pyrolysis front is formed on the wood. This forms a boundary layer between the intact wood and the pyrolyzed material. The pyrolyzing material is considered to char and as the char yield increases, a protective layer is formed. These protective layers may be effective in barring ignition and further charring the wood material. The reaction rate of fire is the rate at which a material is combusted into the products of combustion, such as water, carbon dioxide, and carbon. The rate of fire reaction is determined by three main factors, also known as components of a fire triangle (Raymond Friedman, 2008).

The first three factors that control the rate of combustion are components of the fire triangle. They are heat, oxygen, and fuel. They are heat, fuel, and oxygen. Other factors are the presence of catalysts and the surface area and the nature of the fuel.  The general equation of reaction can be represented as: Fuel + Heat + Oxygen  Combustion products

High moisture content in a material reduces the rate of combustion. Woods with high content of resin will burn faster than those that do not contain resins. The nature of the fibers synthesized by a tree also affects the rate of combustion. Increasing the concentration of oxygen increases the combustion rate. A fuel with a larger surface area exposed burns faster than an intact fuel. Increasing the temperature raises the molecular kinetic energy of both the fuel and oxygen, thus, increasing collisions that increase the rate at which combustion takes place. The presence of chemical catalysts speeds up the rate of the combustion reaction.

Plume velocity – This is the rate at which the plume moves from the fire source to the atmosphere.

Plume rise - The plume rise is the mean vertical height at which a plume will rise most of the time. The height of a plume can be measured by comparing the mean plume height with a known height of an object.

Plume mass – This is a property that measures the mass flow of a plume and can be calculated using the temperature of the plume and its temperature. However, plume turbulence and viscosity make it a challenge to measure plume mass flow (Li & Chow, 2007).

Plume turbulence – In unstable atmospheric conditions, a plume will undergo a transition stage, from laminar flow to turbulent flow as it rises. The instability between warm and cold air causes eddies that roll on the plume.

Air entrainment – This is a plume property that determines the air content of a given plume, and affects the plume mass. A plume with a higher proportion of entrained air will be heavier than a plume with little air entrainment (Karlsson & Quintiere, 1999).

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