2nd International Energy Conversion Engineering Conference AIAA 2004-5539 16-19 August 2004, Rhode Island

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved 1

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EFFECT OF SWIRL ON FLAME CHARACTERISTICS IN FURNACES

Ramiz Kameel, Essam E. Khalil Cairo University, Cairo , Egypt

ABSTRACT

This paper reports the effect of swirling on the transient flame characteristics using a numerical method. A numerical method that is designed to predict the transient flow characteristics in three-dimensional furnace configurations at high Reynolds numbers is incorporated in the present work. Numerical analysis is followed to represent the effects of the swirl number on flow and heat transfer in fire tube boiler furnaces. The effect of air stream swirl on the recirculation zone was also investigated, and is presented in the present work. Radial swirl was found to have an observed significant effect on the flow field. The present study aimed at presenting the furnace flow characteristics under air stream swirl design conditions for optimum effective combustion. The present work made use of 3DTCOMB, a three dimensional time-dependent numerical scheme to obtain a more comprehensive view of the flame development in the different fire-tube boiler furnaces and in power plant boilers with multi-burners. The time dependent results are meant to demonstrate the present numerical capabilities and to assist designers and engineers to pursue optimum design with reasonable cost.

1.INTRODUCTION

The Present mathematical approach solves numerically flow regimes interaction and turbulence characteristics. The governing equations of mass, momentum and energy are commonly expressed in a preset form. The Source terms in the equations represent pressure gradients, viscous action and chemical reactions in these equations. The governing equations are to be solved in the finite difference mode at discritized grid nodes mapping the room. The physical and chemical characteristics of the air and fuels are obtained from tabulated data in the literature. The flow regimes and heat transfer plays an important role in the efficiency and utilization of energy. Kameel and Khalil 1 to be strongly dependent on turbulent shear found the behaviour, mixing, chemical kinetics, wall conditions and geometry of burners. Fluid flow and turbulent characteristics in turbulent combustion chambers play an important role in the thermal balance and performance of the combustor. The fluid flow, recirculation patterns and turbulence cause mixing between different layers in the chamber. It is therefore very important to detect: i . Any recirculation flow zones in the chamber, normally characterized by the existence of eddy of various sizes and strength. These eddies were previously detected, measured and predicted in the open literature for various combustion chamber designs, Khalil 2, Khalil et al 3, Borghi 4 . Non-Intrusive measurements of fluid regimes are approximate and represent major obstacles in adequately verifying mathematical models. ii. Flow regimes in the transverse and longitudinal planes are also influential in combustion and heat transfer performance as these can cause extra mixing and mass transfer within the chamber and aids migration. It is important, however, to analyze carefully the flow pattern in the combustion chamber and to relate the flow to mixing and heat transfer. As seen above, the flow regime is complex and of three- dimensional nature. Previous work to model the chambers flow field was reported in the open literature by Kameel and Khalil 1, Gupta et al5, etc. In simple words the flow is three dimensional, turbulent Recirculatory and complex in nature. Although many investigations had treated the flow as two-dimensional for simplicity, Khalil6, Khalil7, but nevertheless it is primarily three-dimensional. With the advance of computational techniques it is now possible to numerically simulate three-dimensional flows. The results are obtained with the aid of the three-dimensional program 3DTCOMB; applied to combustors. The present numerical grid is a full three-dimensional representation typically 400000-grid node covering the room cavity volume in the X , Y and Z coordinates directions. The numerical residual in the governing equations typically less than 0.001 %. The strength of the recirculation zones; however is characterized by, negative velocities as well as the introduction of the vortices as a measure of flow rotation, and consequent turbulent shear and mixing.

2nd International Energy Conversion Engineering Conference16 - 19 August 2004, Providence, Rhode Island

AIAA 2004-5539

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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2. MATHEMATICAL FORMULATION 2.1.General Three velocity components in X, Y and Z coordinate directions were obtained using a "SIMPLE Numerical Algorithm” [Semi - Implicit Partial Differential Equations Solver] described earlier in the work of Spalding et al 8, Khalil, Spalding and Whitelaw3. The turbulence characteristics were represented by an approximately modified k - ε model to account for near-wall functions. Fluid properties such as densities, viscosity and thermal conductivity were obtained from references. The present work made use of the already available computer Package 3DTCOMB1.The program solves the differential equations governing the transport of mass, three momentum components and energy in three-dimensional configurations .The equations are typically expressed as: ∂ρU/∂t+ ∂ρUU/∂x+∂ρVU/∂y+∂ρWU/∂z = - ∂P/∂x + ∂/∂x(µ∂U/∂x)+∂/∂y(µ∂U/∂y) +∂/∂z(µ∂U/∂z) +Su …….� …(1)

∂ρV/∂t +∂ρUV/∂x+ ∂ρVV/∂y+∂ρWV/∂z = - ∂P/∂y + ∂/∂x(µ∂V/∂x)+∂/∂y (µ∂V/∂y) +∂/∂z(µ∂V/∂z) +Sv � (2)

∂ρW/∂t +∂ρUW/∂x+ ∂ρVW/∂y+∂ρWW/∂z = - ∂P/∂z + ∂/∂x(µ∂W/∂x)+∂/∂y(µ∂W/∂y)+∂/∂z(µ∂W/∂z) +Sw � � .(3) The turbulence closure is assumed through the use of the well known two Equations Turbulence Model. This model was developed in the early seventies by Launder & Spalding 9, assessed by Gosman, Khalil &Whitelaw10 and Rodi11. The Reynolds stresses and turbulent heat fluxes are related through the eddy viscosity concept to the gradients of the mean flow properties via exchange coefficients. The Stresses are expressed in tensor form as: ___ __ __ _ -ρuiuj=µt(∂Ui/∂xj+∂Uj/∂xi)-2/3ρkDij and k=0.5(uiuj) ………(4) Where µt is the turbulent viscosity calculated from the values of k and ε as µt = C� ρ k2 / ε , C� is turbulence model constant =0.09 Dij = Kroncker Delta The values of the kinetic energy of turbulence k and its dissipation rate ε are to be obtained from the solution of their respective transport equations commonly expressed in a similar form to equations 1 to 3. The energy Equation is expressed as: ∂ρH/∂t+∂ρUH/∂x+∂ρVH/∂y+∂ρWH/∂z= ∂/∂x(Γ∂H/∂x) +∂/∂y(Γ∂H/∂y)+∂/∂z(Γ∂H/∂z)+SH ....(5) Where H is the enthalpy, SH is the source of energy due to shear work and internal heat sources. Where Γ=µt / σt and σt is the Prandtl number 2.2.Numerical Procedure The present work made use of an orthogonal Cartesian grid mesh that maps the flow domain. Typical grid sizes of 80 X 60 X 40 nodes were used. The present section describes the numerical results obtained with the aid of 3DTCOMB program developed to predict the flow behaviour under various geometrical and operating conditions. A staggered grid system is employed for the velocities in the Z direction to avoid the decoupling effects between the velocity and the pressure that are frequently observed with the non staggered grid. In the staggered grid domain, velocity components are stored between the pressure nodes along the grid lines. Values of k and ε are stored at the pressure nodes, as shown in Figure 1. More points are concentrated near the walls and where the velocity gradient is expected to be large.

Figure 1: Staggered Grid Arrangement

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2.2.1. Computational Grid Generation The present program utilizes the modified hyperbolic formula of Henkes 12 for grid node generation. The present used formula creates a non-uniform orthogonal grid with dense gird nodes near the walls and internal obstacles. The present program is also designed to simulate the reacting flow domain using 384,000 cells to obtain grid independent predictions with efficient cost13-17. 2.2.2. Numerical Scheme The present program utilizes the both upwind and power-law schemes that proposed 18. The power-law scheme is not particularly expensive to compute and provides an extremely good representation of the exponential behaviour 7. Although the power-law scheme is only first-order accurate on the basis of truncation error, the power-law difference scheme19 is a conservative formulation and does not have the problem of numerical oscillations. The drawback of the scheme is the inherent numerical diffusion. In the recirculating zones, the effective diffusion will be replaced by a numerical cross-flow diffusion in regions of the solution domain where the flow is not aligned with the grid-lines 8,9. 2.2.3. Time-Dependent Procedure This program has the capability to switch between the solving on steady state bases or on unsteady bases. The time interval value is calculated according to the stability condition of the partial differential equation 20. The program is designed to provide storage for the values of variable Φ at time t and at time t + ∆t to employ the iterations within the time step to get the convergent solution within the time step. The fully implicit scheme is utilized in this model. 2.2.4.Initial and Boundary Conditions The initial conditions of the solving domain are taken to represent the actual value of each variable Φ the time t=0. The boundary conditions represent the wall, inlet, and outlet conditions. The detailed treatment of boundary conditions can be found in the literature 1. Near the wall, the log-law of the wall function is applied to correct and find the values of turbulence and dissipation. The velocity of the airflow tends to be zero at the wall surface. 2.2.5.Convergence and Stability The convergence should be attained over the time step. The simultaneous and non-linear characteristics of the finite difference equations necessitate that special measures are employed to procure numerical stability (convergence): these include under relaxation of the solution of the momentum and turbulence equations by under relaxation factors which relate the old and the new values of Φ within the time step as follows: ( ) oldnew 1 Φγ−+Φγ=Φ ……….(6) Where: γ is the under-relaxation factor. It was varied between 0.2 and 0.3 for the three velocity components as the number of iteration increases. For the turbulence quantities, γ was taken between 0.2 and 0.4 and for other variables between 0.2 and 0.6. The required iterations for convergence in the time interval are based on the nature of the problem and the numerical conditions (grid nodes, under-relaxation factor, initial guess, etc.). So the time (on the computer processor) required to obtain the results is based on many factors. The computational time step is selected according space cell (spatial difference) and the airflow velocity over the space cell. The time interval should be small enough to provide the stability of solution over the domain 20. Basically, the increase of the time interval increases the number of iterations over the time interval to obtain the numerical convergence. The initial inlet flow field profiles are assumed in accordance to Khalil13 to adequately represent the true inlet conditions of U, V, and W. The inlet mean velocity components are assumed to be of uniform distribution in the bulk of the inlet grille. The corresponding exit flow conditions are similar in form to those at the inlet conditions. 2.2.6. Data Analyses and Presentations: The program produced massive amount of the data during each of the present investigated cases. Obtained data were about the 105 data point for each case, which were utilized to plot the appropriate vector plots or contours.Kameel 14 lists further details of the data analysis and manipulation routines, figure 2.

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Figure 2: Data Analyses and Manipulation Routines14

To determine whether convergence to steady state has been attained, a relative error, defined as the difference between the values at two successive iteration levels (n) and (n+1) over the value at level (n) for each dependant variable

�, is

monitored with iterations. This continues until the error attains a value less than or equal to 1E-3 while, in addition, the relative error in the overall energy balance becomes less than or equal 0.005. Numerical computations were obtained for convergence criteria of residuals less than a value of 10 -3 of the variable in question . 2.3. Reacting Flow Modeling The present computer procedure was utilized to predict the fluid flow characteristics in the furnace configurations where turbulence-chemistry interactions are strongly present. These where conveniently represented by the Combustion model of Khalil7 . The reaction rate expression strongly depended on the correlation between air and fuel mass fractions fluctuations, turbulence time scale defined in terms of ε/k. The effect of turbulence on reaction rate was characterized by solutions of the transport equations of fuel mass fraction, square of the fluctuations of mass fraction and their correlation. The Heat transfer characteristics were computed from the four-flux radiation model of Khalil and Truelove15. The source term in Equation 5 was obtained from the four-flux radiation model with appropriate treatment of the wall and gas emissivities. 3. RESULTS AND DISCUSSION 3.1.Mean Flow Behaviour The present geometrical configuration represents the flow situations in the furnace of the IFRF data published by Bartelds et al 16 .The furnace configurations were of 2x2x6 m firing natural gas at a firing rate of 2.96 MW with excess air of 4% relating to flame 29. The measured and predicted heat flux distributions along the furnace walls are shown in Figure 3. The previous two-dimensional predictions of Khalil 13 are shown by the dashed curve while the present three-dimensional predictions are shown by the solid curve. Both measured and predicted distributions are in relatively good agreement considering the experimental error and modelling assumptions. A second comparison case was carried out for the configuration of Hutchinson et al 17. Their experimental results were obtained in a cylindrical vertical combustor whose inner diameter was 0.3 m and length of 0.9 m. The furnace was fires with natural gas of 94.4% CH4 and was water cooled in five separate segments, with the burner plate also water cooled. The coaxial burner had a central fuel jet of 0.012 m and the annulus had inner and outer diameters of 0.027 and 0.055 mm used for combustion air flow. A vane swirler of swirl number of 0.52 was used. Figure 4 shows an example of the radial profiles of mean axial velocity at various axial locations downstream the burner for swirl number =0.52 . Two-dimensional predictions of Hutchinson et al 17 are shown in Figure 4 together with the present three-dimensional predictions to be in good agreement with the corresponding measurements. The corresponding radial profiles of the gas measurements are shown in Figure 5 with the predictions obtained with two and

Data

Graph Fortran Program

Plotting Programs

Case Study Batch

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three-dimensional computational procedures. Local values of temperature profiles were shown to be in qualitative agreement with the corresponding experiments. The three present three dimensional computational schemes yielded better agreement with the measurements for swirling flames. 3.2. Power Plant Boiler Simulations A real practical application of furnace design is for water tube boilers with vertical water walls, multi-gas fired burners. The present section demonstrates the capabilities of the present program to readily predict turbulent reacting multi-flames emerging from four burners’ matrix. The present simulation is for a boiler of rated capacity of 100 ton/hour steam at 87 bar, 520 0 C. The boiler furnace was 4.0x4.0x10.m, post combustion gases are then allowed to flow into a second conduit where heat is transferred to typically simulated superheaters, reheaters, feed water heaters and air reheaters out to stack. In the present simulation no physical blockage of these heat exchangers were predicted but only their heat transfer and fluid flow pressure drops were accounted for. Figures 6 and 7 demonstrate the predicted velocity vector plots and temperature contours at start up and normal running after 120 seconds conditions. 4. CONCLUDING REMARKS From above one may conclude that turbulent flow patterns and heat transfer characteristics in furnaces are strongly dependent on swirl intensity, turbulence and time progress from start-up to steady state. More maximum absolute velocities and higher turbulent characteristics are demonstrated in situations with swirling jets in single and multi-burners. It can be concluded that: The present three-dimensional modelling capabilities can adequately predict the local flow pattern in turbulent combustors. Predictions demonstrate flow patterns that are similar in form but differ in details at different operating conditions. Turbulence characteristics as identified here by the shear stresses indicate that higher turbulence level appears in the vicinity of reaction zones. ACKNOWLEDGEMENT Technical discussions and assistance of our colleagues at Cairo University are highly appreciated. REFERENCES 1.Kameel R.,and Khalil E.E. , (2004) “Heat Transfer Characteristics In Furnaces: Effect Of Combustion And Heat Transfer Modelling”. AIAA Paper AIAA-2004-0803, Jan.2004 2.Khalil E.E. (1977) Flow, Combustion & Heat Transfer in Axisymmetric Furnaces,(1977) PhD. Thesis , London Univ. 3.Khalil, E.E., Spalding D.B. and Whitelaw, J.H. (1975) The Calculation of Local Flow Properties in Two-Dimensional Furnaces, int., Heat & Mass Transfer, Vol.18, pp775. 4.Borghi , R. Computational Studies of Turbulent Flow with Chemical Reaction ,Project SQUID on Turbulent Mixing. ,AGARD CP125. 5. Gupta A.K. and Lilley, D.G. (1985) Flow field Modeling and Diagnostics. Abacus Press , 1st Edition. 6.Khalil E.E. (1980) On the Modeling of Reaction Rates in Turbulent Premixed Confined Flames,AIAA–80-0015. 7.Khalil E.E. (1986) Numerical Calculations of Turbulent Reaction Rates in Combustors ASME 86-WA/HT-37. 8.Spalding, D.B. and Patankar, S.V. (1974) A Calculation Procedure for Heat, Mass and Momentum Transfer in Three Dimensional Parabolic Flows. Int.J.Heat & Mass Transfer, Vol.15, pp1787. 9. Launder B.E. & Spalding D.B. (1974) The Numerical Computation of Turbulent Flows, Comput.Methods Appl.Mech., pp269-275. 10. Gosman, A .D . , Khalil.E.E. & Whitelaw, J.H.(1979) The Calculations of Two Dimensional Turbulent Recirculating Flows , Turbulent Shear Flows ,Springer Verlag ,13-35. 11.Rodi, W.G., (1984) Turbulence Models and Their Applications in Hydraulics-A State of the Art Review. IAHR , Delft, Netherlands. 12.Henkes .R.W.M ,(1990) Natural Convection Boundary Layers ,PhD. Thesis , Delft University ,Netherlands. 13.Khalil E.E. (1983), Modelling of Furnaces and Combustors. Abacus Press, 1st Edition, U.K., 1983.

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14.Kameel, R.,(2000) Computer Aided Design of Flow Regimes in Air Conditioned Spaces, MSc.Thesis ,Cairo University 15.Khalil E.E. and Truelove,J.S. (1977) ,Calculations of Heat Transfer in a Large gas fired Furnace, Letters in Heat and Mass Transfer ,4,pp.353-365. 16.Bartelds,H,Lewis,T.M.Michelfelder,S.and Pai,B.R. (1973) Prediction of Radiant Heat Flux Distribution in Furnaces and Its Experimental Testing,IFRF Doc.G02/a/23. 17.Hutchinson, P, Khalil, E.E., and Whiltelaw, J.H. (1980) The Calculations of Flow and Heat Transfer Characteristics of Gas Fired Furnaces Proc.18th Symp. (Int.) on Combustion, pp.1927-1931. 18. Patankar, S. V. (1980), Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, WDC. 19. Sorensen, D. N., and Nielsen, P. V., (2003), Quality control of computational fluid dynamics in indoor environments, Indoor Air, Volume 12 No.1, page 2. 20.Leonard, B. P., and Drummond, J. E., (1995), Why you should not use ‘hybrid’, ‘power-law’ or related exponential schemes for connective modelling – there are much better alternatives, International Journal for Numerical Methods in Fluids, 20, 421-442, 1995. NOMENCLATURE k Kinetic Energy of Turbulence Ma ,ma Mean and fluctuations of species (a) mass fraction , P Pressure S Swirl number (tangential to axial Momentum Su ,Sv ,Sw Source terms in governing Equations of U,V,V T, T’ Mean & fluctuations of Temperature U,V,W Three Velocity Components in X,Y,Z Coordinate Directions u,v,w Three velocity fluctuations in the X,Y,Z Coordinate Directions X,Y,Z Coordinates Directions ρ Local density µ Local viscosity ε Dissipation Rate of kinetic energy of Turbulence Subscript fu identifies fuel stream

Figure 3: Wall Heat Flux Distributions for the Furnace of Bartelds et al 16

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0 1 2 3 4 5 6 7X, m

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Khalil [13] 1 Clear + 2 GreyKhalil [13] k = 0.1Khalil [13] k = 0.2Expt.3D Present Work

Flame 29

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Figure 4: Furnace Axial Velocity Profiles7 Figure 5 : Furnace Gas Temperature Profiles

m/s

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