Of Fluids, Fire, Heat, Dimensional Analysis, and Turbulence - Assignment Example

FV2001 ASSIGNMENT Name: Professor: Institution Name: Date: FV2001 Assignment 1. Classical Mechanics of Fluids Q 1.1 When the motion of fluids is studied macroscopically, it is observed to appear structurally continuous. The Navier-Stokes equations describe fluid flow in relation to fluid pressure, velocity, density, temperature and viscosity in a flowing fluid (Bhavikatti, 2008). ) = 0, (Continuity equation) = + F + u, (Equation of motion) + u. u = 0, (Conservation energy) + u.u u.u) + g, (Momentum equation) Where: u = the velocity vector = thermodynamic energy P = pressure T = temperature = density of fluid = dynamic viscosity of the fluid = the coefficient of heat conduction F = external force acting on the fluid per unit mass g = gravitational acceleration per unit mass The equation of motion requires turbulence motion. Turbulence models are significant since it is difficult to capture every scale of motion directly. In addition, steady state solutions are preferred to detailed and time accurate motions. Unsteady motions cannot be resolved, hence, require modelling. An example of the source term in the energy conservation equation is the velocity vector. Turbulence models are necessary because we cannot afford big enough computers to directly capture every scale of motion. Also, users of CFD typically want a steady-state solution (with all the unsteady fluctuations averaged out) rather than a detailed time-accurate one that captures every little vortex. As a result, there are unsteady (turbulent) motions affecting the flow that cannot be resolved directly; they must therefore be modeled (DiBenedetto, 2010). Q 1.2. and Q1 = Q2 Q2 = 2V2 So, A2 =Q2 X 2/Q = 2Q The equation of pressure drop is: (P1-P2) = = = 111.1125 Pa Hence, pressure drop = 111.1125 Pa. 2. Dimensional analysis (25 marks) Q 2.1. a. = No units b. c. d. e. The terms in (a) above are non-dimensional. Q 2.2. The velocity depends on kinematic viscosity, specific dissipation and fluid density. Therefore, V=vaεbρc (equation1) [L/T)= [L2/T] a [M/LMT] b [M/L3] c Comparing the dimensions on both sides, we have: For L 1=2a –b -3c For T: 1 = -a-b For M: 0 = 3c Therefore, c = 0, b=1/3 and a=2/3 Substituting the values of a, b and c in equation 1: VT = . 3. Heat Transfer, Thermochemistry and Fluid Dynamics of Combustion (25 marks) Q 3.1 When PMMA is ignited at 460 °C, it burns to form Carbon dioxide, carbon monoxide, water and compounds including low molecular-weight formaldehyde. A sheet of PMMA continues to burn if not put off. Energy is released in the process of combustion. Calculating the stoichiometric fuel-air ratio One molecule of PMMA = 5(12.01) + 8(1.008) + 2(16) = 100.114 Six molecules of oxygen = 6(16) = 96 So, fuel-air ratio = (100.114/96) = 1.0429 This means we need 1kg of oxygen to burn 1.0429 kg of PMMA. Since the air contains 23.2 mass percent of oxygen, Stoichiometric fuel-air ratio = 1/1.0429(100/23.2) = 5.27 Heat produced when 2.5 kg of the fuel is bunt = (2.5 x 24.9) = 62.25 MJ Q 3.2. The reaction rate of fire is defined as the rate at which heat is released per unit area and time. It is expressed as energy/area/time (Rana & Joag, 2011). Factors affecting the reaction rate of fire The type, size and surface area of the reactants will influence the rate of chemical reaction. A larger surface area increases the rate of reaction of reaction. The concentration of the reactants: The rate of secondary reaction increases with increase in concentration of the reactants. Time of reaction: As time goes by more and more reactants react to form the products. Rate of primary reaction: Generally, if the rate of primary reaction is high, the secondary rate of reaction will be relatively high (Drysdale, 2011). An example of a secondary reaction involves the formation of caustic soda: Na + H2O =NaOH + H 4. Characteristics of Flames & Fire Plumes Q 4.1 Characteristics of fire plume Mean plume height: This is the average vertical height at which plumes are observed to appear most of the time. At flame height, intermittency is equal to 0.5. The plume height or the flame height may be measured by comparing the plume with a known measurement of an object. The correlation of flame height is given by Heskestad equation below: Plume Turbulence: As the plume rises, there is transition from laminar to turbulence flow brought about by atmospheric conditions. Laminar flow is observed in small flames. Eddies roll on the outside of the plume, being caused by the instability between the cold and hot air. The Froude’s number determines the nature of flow. It is given by: Froude’s number = Where: u = velocity of plume D = diameter of the flow source The higher the Froude’s number, the more buoyant is the plume rise. Plume mass: This is the mass flow of plume calculated from the velocity and temperature of the plume. Turbulence and discontinuity of the plume may make it difficult to measure mass flow. Air entrainment: The amount of air entrained in the plume determines the weight of the plume, thus, the more air is entrained, the heavier the plume. Heat release rate: This is the amount of thermal energy released into the atmosphere per given time. The axisymmetric plume model is based on diffusion of the plume. A symmetrical line of axis is assumed along the vertical centerline, where the temperature is maximum and decreases towards the edges of the plume (United States. National Fire Prevention and Control Administration, 1976). Q 4.2 Factors that can affect the spread of flame Density of the fuel materials: The density of the flame affect the speed of spread of fire is spread. Plastics and woods, with high density, and of the same generic type will conduct more heat energy from the ignited fuel more rapidly compared to the same materials of low density. The high density materials have insulating properties that allows heat to stay at the surface and limit spread of fire. For example, Low density foam plastic material ignites quickly and spreads fire faster than a higher density plastic of the same material. Light fuels will ignite rapidly and cause the fire to spread quickly compared to heavy fuels. The size, amount and surface area of the solid fuel: The size of the fuel relates to how quickly fire spreads in the compartment. A larger size of fuel will spread fire faster than a small size of fuel. The amount of combustible fuel available for burning is referred to as fuel load. The higher the fuel load, the more heat will be released and thus, rapid fire spread. On the other hand, the larger the surface area of the fuel, the more interactions of oxygen molecules and the fuel surface will occur per given time, making the combustion process faster. High surface area to mass ratio nature of combustible materials make them more easily burned. For example corners of materials are easily burned than materials with flat surfaces. Availability of oxygen: The rate of burning will be affected by the amount of oxygen available. The lower the concentration of oxygen in the compartment, the slower the rate of burning and fire spread. Increased oxygen supply favors more reactions between oxygen and the fuel, thus, the fire will continue to spread. Amount of thermal energy produced: What is made of the fuel determines the amount of energy released into the atmosphere when the fuel is burned. Different fuels react differently with oxygen, and will have varied amounts of energy produced depending on the rate of reaction. Moisture content of the fuel: The rate of ignition and burning of a given fuel is also determined by the amount of moisture contained in the fuel. The drier the fuel, the more rapid it burns (Drysdale, 2011). References Read More