Hamad Fluid Dynamics - Lab Report Example

Question1: Classical mechanics of fluids The Navier-Stokes Newton’s second law of motion by applying the pressure term as well as the stress in the viscous fluid to govern fluid flow in fires. The Navier-Stokes equations include the following. a. Stokes’s stress constitutive equation For elastic and incompressible solids the expression used is given as; In this expression; Referring to the strain-tensor rate Stokes’s stress constitutive equation for fluids that are viscous and incompressible is given as: In its convective form, the equation becomes; Where; Constitutive equation that’s is applied to elastic solids that consider linear stress is given as; In which; For elastic solids, the constitutive equation is given as; The constitutive equation for linear stress in thermal hydraulics is given as; Where; Where µ and remain constant in the equation. The momentum equation is given as; In which, the bulk density is to be constant throughout. P is given as; The value of is given as zero. b. The Cauchy momentum equation The Cauchy momentum equation expresses the conservation form of the momentum. The equation is given as; c. Momentum equation The moment equation is obtained by getting the product of mass and the velocity. The expression below is obtained by substituting in the mass conservation equation. Given, Then the expression below is obtained; In the given equation, the left expression is always equated to zero and it refers to the mass continuity. Resulting to the expression given below; The expression can also be expressed as given below by applying the derivative operator and it refers to the Newton’s second law of motion; In the equation for momentum conservation, the following terms need turbulence modeling. i. The velocity of the fluid flow () ii. The flow expansion rate () iii. The fluid density (ρ) iv. The tensor product ( Turbulence models A turbulence model is very important in calculating the mean of flow directly without following the normal procedure of first considering the flow field that has full time-dependent properties. When considering the fluid mechanics, a vortex refers to a region in which the fluid flows around a line axis in a fluid. The line of axis in this case can either be curved or straight depending on the region considered. In turbulent flow, the vorticity as well as the velocity distribution are the major components used to determine the vortices characteristics. A figure that can be used to give a summary of the analysis of scales of vortices is given below; Figure 1: scales of vortices analysis Energy conservation equation Energy equation The energy equation is given below; Where; 1.2 Vertical riser Given that; The diagram below is used in solving the questions Figure 2 The given parameters are as follows; Applying the Swamee-Jain equation, But, Then; Since then the flow is turbulent. From the Swamee-Jain equation; Therefore; Applying Bernoulli’s equation between 1 and 2, it becomes, The Bernoulli’s equation is given as; But, is zero, thus, Therefore; But; Without friction, the Bernoulli equation becomes; Question 2 Dimensional analysis 2.1 Dimensions Let Therefore; 2.1 Kolmogorov scale of velocity The Kolmogorov length scale is considered in this case. It is given by; Assumption, rate of energy dissipation is the same at all the considered length of scale, then In which; Introducing the Reynolds number to the equation; It therefore indicates that; Referring to this dimensional analysis the relation among the three main parameters is obtained Question 3 Heat Transfer, Thermo chemistry and Fluid Dynamics of Combustion 3.1 Burning of wood Wood is one of the organic materials in nature. Its burning involves a number of processes that include; Pyrolysis Charring Flaming Heat transfer The processes of burning of wood are discussed below; Pyrolysis process Pyrolysis refers to an organic material’s thermochemical decomposition at temperatures that are elevated devoid of oxygen and/or any halogen. This process is entirely reversible and it involves a change of chemical composition as well as physical phase that is simultaneous. This process mainly used in the chemical industry to produce charcoal, methanol, activated carbon and other wood chemicals. Charring Charring refers to a process (chemical) of combustion that is incomplete of wood when subjected to heat that is high. Char is therefore, the residue matter that is remains in this process. Charring mainly removes oxygen as well as hydrogen from wood. Therefore, the remaining char is composed of carbon. In the burning of wood, char result from fire, which is a naturally occurring process. Flaming A flame is the part of fire that is both visible and gaseous. Flaming results from a reaction that is highly exothermic. The flames that are cooler are mostly red in color and produce the most smoke. This can be attributed to lower temperature during the burning of wood. Heat transfer Heat can be transferred from one point to another through many methods. The major methods involved in heat transfer include; conduction, convection and radiation. The temperature difference between the hot and cold part therefore, plays a major role in the heat transfer in wood. When the temperature difference is high, the rate of heat transfer will also be high and vice be versa. 3.2 Reaction rate of fire Reaction rate of fire refers to the how quickly or slowly that the fire reaction takes place. A typical chemical reaction is be given as; The factors that affect the reaction rate in a general secondary order chemical reaction include; Nature of the reaction: this refers to the physical state of the reactants, reaction complexity and the number of the species that are reacting. Temperature: a high temperature increases the number of collisions between particles therefore increasing the rate of reaction and vice versa. Concentration; the rate of reaction increases with increase in concentration because the collision frequency increases. Pressure; in gaseous reaction, the rate of reaction increases with increase in pressure because the number of reactant collisions increases. Order; this mainly affects how the concentration of the reactant as well as pressure in gases affects the rate of reaction. Catalyst; the presence of a catalyst increases the reaction rate. Methane gas is considered for the chemical reaction of a gaseous fuel. The chemical reaction is as given below; In the above equation therefore; When comparing with the general equation provided earlier. 4. Characteristics of Flames & Fire Plumes 4.1 Fire plumes A fire plume is a burnt gas column that is formed as a result of fire. The main characteristics of the liquid fuel pool fire plume are temperature and flow speed. Therefore, the temperature experienced at a certain radial distance is less than the temperature at the centerline of the plume. The other types of flows encountered in the fire plume include; The plume mass flow rate: refers to the total mass flowing within the boundaries of the plume at a particular height in the upward direction. Plume flow velocity: refers to the highest velocity experienced at the plume centerline. It increases with the plume height in a flame region that is continuous Axisymetric plume model; should consider the main factors that affect the smoke production rate and the temperature. The main factors of interest should be the main openings available and the plume height. 4.2 Diffusion flames A diffusion flame is a type of flame in which the flame combustion is experienced at the surface only. The surface at which combustion takes place has the right concentration of oxygen. Combustion occurs when the fuel meets oxygen. In this flame therefore, unburnt fuel exists in the flame’s interior. References Fluid Mechanics 4th by Frank M. White Fluid mechanics 5th edition by John G.Douglas ,2005 Glassman,Irvin; Yetter,Richard A.(2008) .”Diffusion Flames”. Heskestad . G. Fire Plumes, Flame Height, and Air Entrainment. SFPE Handbook of Fire Protection Engineering. 4th ed,2008. Kreith, F.; Berger, S.A.; et. al. “Fluid Mechanics”Mechanical Engineering Handbook Ed. Frank Kreith Boca Raton: CRC Press LLC, 1999. Read More