Computing fluid dynamics on burner air flow in natural draft furnaces

The mean key variable to control the burner performance for safe and efficient operations is the amount of excess air or oxygen which flow to react with fuel. In accordance with Typical Draft Profile in a Natural Draft furnace the numerical results of computing fluid dynamics model of the air flow from the environment to the burner by adjusting the area of air box prototype openings will give the necessary information to adjust the performance of burner as optimum. The model of air box prototype is useful tool in applying similarity theory on another burners̕ designs which depends the air box tools to calibrate the quantity of combustion air flow to the burner. Keywords— excess air, air box design, computing fluid dynamics, natural draft furnaces.


INTRODUCTION
In many burners of natural furnaces today there are insufficient means to adjusting the ratio of fuel to air, the key variable to control the burner performance for safe and efficient operations is the amount of excess air or oxygen which flow to react with fuel. While some excess oxygen is necessary to have safe operation, too much oxygen wastes fuel, energy, and heat. The Air box is one component of burner which is used to control the amount of air excess by modifying its air registers. So the numerical results of computing fluid dynamics of the air flow from the environment to the burner by the air box will give the necessary information to adjust the performance of burner as optimum. In result; the process engineer will not depends on the laboratory analysis about the flue gas data from all sides of the combustion chamber of furnace at each burner. That is because the numerical results give a lots of information about the air flow through the air box to burner and its quantities from a design point to the operating case as a result of coupling the average velocity of combustion air which enter from the gats of air box into burner with the pressure arise across the burner or the air box.
The pressure arise across combustion equipment like a burner etc., can be calculated from the following equation [1] ∆ = 2 2 U = velocity of air at burner exit m/s K is the flow resistance factor where K=1.5 for tangential burner and K= 3 for swirl burner of gas and heavy oil [1] But from operation point, the air flow rate in burner can calculated from [1] = . ₒ ( ).

+ 273
The flow of air m 3 /s ₒ Theoretical air flow Nm 3 /kg Fuel feed rate kg/s Excess air coefficient at furnace outlet (there is not leakage into furnace) Air temperature • C So the numerical results information which are gotten from the prototype air box can be used to predict the quantity that may be enter from the doors of the air box by using the theory of dynamics similarity which related by the Reynolds number of the air flow into the burner at all times with its Reynolds number at design case. From a design point these gates must provide enough air for fuel's burning process. The correlative with maximum amount fuel consumption and surface area of all gates is defined by [2] ( ) = × × × Maximum amount fuel consumption Amount of air providing for burning the fuel Area of activated gate = 1 in this case study Discharge consumption coefficient 0. 6-0.75 Air speed through gate 0.5 m/s Here the process engineer thinks that in fact the excess air does not related only by adjusting the air box registers because it is important to maintain the correct furnace draft. So too little draft can damage the metal structure and snuff TO benefit from the numerical results information which are gotten from the prototype air box from a design point, the process engineer must begin to ultimate the pressure arise across the burner (draft available at burner level),and he must follow these general rule which are mentioned for any duct in furnace not only for burner . 1-General Rules to ultimate the pressure arise across any air duct in furnace By adding the natural draft components of all parts of the air ducts, the total natural draft ∑ is obtained, so the total pressure drop ∆ in the air ducts in the furnace can be obtained by subtraction [ Is the total pressure drop in the air ducts in the furnace, Fig.(2) Shows typical draft Profile in a natural draft furnace ∆ Is the total pressure drop after correction of elevation.

∆ = ∑ ∆ 101325
The sum of resistance of all parts of the air duct gives the total resistance of the air duct∑ ∆ .

2-Mathematical model on air flow into swirl burner as case study
The burner used in this study consists of two concentric tube with a tangential and radial swirler placed in annular arrangement.  desired internally staged flame, the burner utilizes swirl induces centrifugal body forces to dampen turbulent exchange between the fuel and air stream allowing an extended residence for fuel conversion chemistry in locally fuel -rich environment prior to burn out [4].The NOx emission is at its peak at stoichiometric conditions when other pollutants, like CO and VOC, is at its minimum (see Fig.(3)).This is mainly because of the strong relation between temperature and thermal NOx production [5] Fig. 3: NOx formation rate driven by temperature at equivalence ratio and Schematic drawing of (a) air staging, and (b) fuel staging [5] NOx reduction needs to apply correct operating parameters and used as a design basis, so in accordance with NOx reduction work, it is essential that excess air levels be reduced to close to 2-4% O2 as all NOx emissions are corrected to3% O2 (see fig. (4)) [3]. The most significant useful phenomenon of the swirling flows is the existence of internal recirculation zone IRZ which aids in flame stabilization by providing a storage of hot flow flue gas, so its flow field is thank for its effect in internal flue gas recirculated to the combustion zone to reduce the NOX emissions, by reducing the oxygen concentration as well as lowering the flame temperature. In internal FGR, the fuel gas is recycled into the flame zone due to burner aerodynamics [5] Fig. 4: Excess Air vs. Oxygen Content in Flue Gas (A) [3] and typical low NOX swirl burners̕ flow field with internal staging schematic (B) [4]   In result, combustion product are recirculated and by this phenomena reduced velocity region is created, the boundary of the recirculation eddy is determined by the radial points at which the forward mass flow equals the reverse mass flow at the axial station so the region which is enclosed where the axial velocity reaches zero magnitude in each axial plane [6]. Ambient air temperature, pressure and humidity affect the air flow rate if the air temperature increases the air flow rate decreases. As definite temperature, pressure and humidity of air increase, water vapor in ambient air is decreased and leads to decrease of the percentage of O2. So the air flow rate through the air box at definite pressure drop by using correspondingstate is defined by [7] = √ 2 ∆

International journal of Chemistry, Mathematics and Physics (IJCMP)
[ Air mass flow rate kg/s, g Gravitational constant 9.8kg/s 2 , Cross section area in internal cylinder m 2 , ∆ Air side pressure drop across air box in pascal (natural draft is available at air box level), Pressure loss coefficient through air box and can be estimated as equal to 0.6-0.75 -Cold mathematical model flow of vertical air box: As in the case of any problem in flow filed this particular type of flow described by the mathematical expressions of continuity and momentum in Cartesian coordinates: Continuity equations: ∂u ̅ ∂x + ̅ + ̅ = 0 Momentum Equations: In this situation the body force with constant density equals to the balance between the driving force of buoyancy and the initial hydrostatic pressure, so at any point in the fluid domain the equation of motion is: Where: is the actual temperature applicable locally. ∞ : is the undisturbed constant temperature. : is the coefficient of the thermal expansion of air and by using the equation of stat for the perfect gas = Where is universal gas constant, is the local static pressure, and is the local density so ( = 1/ ), T is the Reynolds stress tensor divided by the density and it is computed by using the Boussinesq model equation

Where is the turbulent kinetic energy, is Kronecker
Delta Function, Then the letters i, j, k ...can be used as variables, running from 1 to 3 so Instead of using x, y, and z to label the components of a vector, we use 1, 2, 3 and Τ is the turbulent eddy viscosity can be calculated by K-Epsilon model so is constant equals to 0.09 These models are not valid near wall to model wall effect so wall function have to be employed.
-Wall y+ Strategy for Dealing with Wall-bounded Turbulent Flows for air box geometry: A wall y+ in the range of 30 to 60 is determined to be sufficiently accurate. Where the log-law region is resolved.
It is also advisable to avoid having the wall-adjacent mesh in the buffer region since neither wall functions nor near wall modelling approach accounts for it accurately, so for the existence of deferent boundary layers in air box geometry enhanced wall function is used -Boundary condition: Here the air box was opened to the environment from surrounding sides of the gates at the maximum fuel gas consumption which it was = 0.02 3 / and ( = (

II.
RESULTS AND CONCLUSIONS The wall y+ is a non-dimensional number similar to local Reynolds number, determining whether the influences in the wall-adjacent cells are laminar or turbulent, hence indicating the part of the turbulent boundary layer that they resolve [8], and it can be seen below as well as Velocity vector plots, can be seen below in the photos of Fig. (a), (b) and (c). These plots give a lot of information about the flow field of the air box of the burner. The recirculation at the corners of air gates and air flow by the area of gates is also obvious from these figures. The air combustion tends to move into the air box by natural draft of the furnace at its level.

International journal of Chemistry, Mathematics and Physics (IJCMP)
[

Fig.c: y+ and velocity vector plots in the field of air box for solution 3.
Solution 3 by iteration method at a steady state-physical relaxation step equals to 0.05 sec, the convergence criteria of RMS residuals is 0.0002, first order is used for advection scheme, distorted fluid elements are 331 elements , and the following

2.78×10
The comparison between these three solutions emphasis that solution 2 is preferred. That is because it gives the necessary information by the best computing cost as it is clear from fig. (c) Which shows the same velocity profiles for the three solutions at the same path.   In fact, by industry these kinds of air boxes are used as tools to adjust the fuel /air ratio in many burners' designs which work on natural draft as it can be seen from fig. (e) Which shows low NOx burner with physical separate between two stages (two air stages and two fuel stages). Here burner depends on two air boxes for natural draft of the combustion air. So in result this model for air box in the low NOx swirl burner which is studied is too useful to get the important information and calibrate another burners performances by using the similarity theory as dynamics and geometry parameters, or to build different air boxes models by the same methodology to get the best from the system as large efficiency and less pollution especially for adjusting NOX emissions.