Appendix Papers presented in ICCFD5 but unpublished

in ‘Computational Fluid Dynamics 2008’

Analysis of free-shear flow noise through adecomposition of the Lighthill source term

Florent Margnat1, Veronique Fortune2, Peter Jordan2 and Yves Gervais2

1 Laboratoire SINUMEF, Arts & Metiers ParisTech, 151 boulevard de l’Hopital,75013 PARIS, France. florent.margnat@paris.ensam.fr

2 Laboratoires d’Etudes Aerodynamiques, UMR CNRS 6609, ENSMA, Universitede POITIERS, Bat K, 40 avenue du Recteur Pineau, 86022 POITIERS Cedex,France. [veronique.fortune, peter.jordan,

yves.gervais]@lea.univ-poitiers.fr

A decomposition of the Lighthill source term ∇ · (∇ · (ρu⊗ u)) is performedwith view to more clearly understanding the mechanisms which underlie theproduction of flow-induced noise. Observation of source fields and associatedradiation patterns leads to 3 main observations: 1) the amplitude of subtermsin the source field does not scale with the associated acoustic contributions;2) balances and destructives interferences are present between subterms; 3)source behaviour associated with convection and sound-flow effects is high-lighted.

1 Context

The mechanisms of acoustic wave generation by unsteady flows still have notbeen fully understood. In the formalism of acoustic analogies, the acousticperturbation in an ambient medium is viewed as excited by the flow move-ment acting like external sources. The source term is a consequence of theNavier-Stokes equations which govern the whole fluid domain/movement. InLighthill’s theory [1], the acoustic perturbation is described by a wave equa-tion, the source term is given by the right-hand side of eq. 1.

∂2ρ

∂t2− c20∆ρ ≈ ∇ · ∇ · (ρuu) (1)

This equation provides a means to extract noise from a known flow, but thesource-term expression offers poor information about the physical mechanismsresponsible for the production of sound. The objective of the present studyis to examine the various physical phenomena which make up the Lighthillsource term, and to see the extent to which this analogy can help us under-stand the mechanisms which underlie the production of sound by free shear

2 Florent Margnat, Veronique Fortune, Peter Jordan and Yves Gervais

flows. Similar attempts have been made by Bodony & Lele [2] who evalu-ated source term competition in the whole Lighthill equation (including theentropic term).

2 Methodology

A decomposition of the Lighthill source term [3] into 10 sub-terms (equation 2)is proposed, in which the velocity u, vorticity ω, dilatation Θ and density ρfields appear explicitly.

∇ · ∇ · (ρuu) = ρu∇Θ︸ ︷︷ ︸1

+ ρΘ2︸︷︷︸2

+2Θu∇ρ︸ ︷︷ ︸3

+ ρ∆u2/2︸ ︷︷ ︸4

+∇ρ∇u2/2︸ ︷︷ ︸5

+ ρu · ∇ ∧ ω︸ ︷︷ ︸6

+u · ∇ρ ∧ ω︸ ︷︷ ︸7

− ρω · ω︸ ︷︷ ︸8

+u · (∇∇ρ)u︸ ︷︷ ︸9

+u⊗∇ρ : ∇u︸ ︷︷ ︸10

(2)

Thus written, the Lighthill source term can already be linked to vorticity-based acoustic analogies of Powell [4] and Howe [5] : terms (4 + 5) are thecompressible form of the kinetic energy Laplacian, and terms (6 + 7 + 8) arethe compressible form of the Lamb vector divergence. We note also that only 3terms [4, 6, 8] would remain in case of an incompressible assumption, becausethe other ones contain either the density gradient or the dilatation.

This decomposition is now tested in a 2D mixing layer flow. Firstly, adirect acoustic simulation is performed, providing a reference solution as wellas source data. Secondly, the acoustic emission of each sub-term is predictedand analysed using Green’s solution of the inhomogeneous wave equation.

3 Numerical approach

3.1 Direct Acoustic Simulation

The compressible Navier-Stokes equations are solved in a computational do-main which includes both aerodynamic and far-acoustic fields of the flow. Theequations are written in a non-conservative form for the primitive variables p,ui and s, which are respectively the pressure, the velocity components and theentropy of the flow. In the characteristic-based formulation used here, the in-viscid part of the equations is expressed as a decomposition into several wavemodes of propagation, in order to facilitate the treatment of non-reflectingboundary conditions. Sixth-order compact finite differences are used to com-pute spatial derivatives, while time marching is performed by a fourth-orderRunge-Kutta scheme.

The spatial evolution of a two-dimensional mixing layer is considered wherethe two streams have initial velocities U1 and U2. The x− and y− directions

A decomposition of the Lighthill source term 3

denote respectively the streamwise and transverse directions. The initial meanstreamwise velocity is given by a hyperbolic-tangent profile, with U1/U2 = 2.A small amplitude, incompressible disturbance field is added at the inflowboundary to initiate the transition process. The mixing layer is forced at itsmost unstable frequencies in order to control the roll-up and vortex pairingprocess. A sponge zone is added to dissipate aerodynamic fluctuations beforethey reach the outflow boundary and to avoid any spurious reflexion (seeMoser et al. [6] for more details).

The present results are from a simulation of a mixing layer with a Reynoldsnumber Re value of 400 and a Mach number M value, based on the differenceof the initial velocities U1−U2, of 0.25. The size of the computational domainis Lx = 800 × Ly = 800 and the grid resolution is nx = 2071 × ny = 785(detailed description of geometry and grid can be found in [7]).

3.2 Computation of acoustic field through Lighthill’s analogy

We compute an acoustic pressure field as given by the integral solution ofequation (1) :

pa(X, t) =1

4π

∫V

S

(x, t− |X− x|

c0

)dVx

|X− x|(3)

where pa is the acoustic pressure fluctuation at the observer position X,V is the source volume, S is the source term defined in (1) or one set of thesub-terms defined in (2) and is assumed to be zero outside V , x is the sourcepoint position. The solution of (3) is obtained by using the 3D Green function.

An advanced-time approach enables a single reading of the source datafiles. The interpolation at the retarded-time is performed using a Hermitescheme in which time derivatives are extracted from the direct computationusing a centered scheme of 4th-order in ∆t.

The source terms and their time derivatives are saved from the directsimulation and sampled at each 10∆t which corresponds to Tp/50 where Tp isthe period of vortex pairing in the mixing layer. A damping function providesthe outflow condition downstream from the pairing process as well as thecancellation at the other boundaries of V . The radiation of the mean field ofthe source term is also computed and substracted from the total radiation inorder to get centered acoustic signals.

Finally, acoustic fields are obtained computing (3) for 150× 150 observerpoints uniformly spaced by c0Tp/15. A recursive algorithm is designed in orderto optimise the acoustic picture construction.

4 Results

In figure (1) the acoustic field predicted by the Lighthill formalism iscompared to the reference solution given by the compressible DNS.

4 Florent Margnat, Veronique Fortune, Peter Jordan and Yves Gervais

Fig. 1. Acoustic pressure fluctuation fields for a Mc = 0.375, Re = 400 mixinglayer. Left: direct computation (reference solution); middle: result from Lighthill’sanalogy with limited source domain; right: result from Lighthill’s analogy with sourceintegration over the whole DNS domain.

A good agreement is obtained when the integration of the volume source iscarried out over the whole DNS domain. Otherwise, the acoustic field exhibitsan incorrect wavefront pattern.

In figure (2), the relative amplitudes of the subterms are summarisedthrough histograms representing their level of variation with respect to thatof the total source term, for the source quantities in the vortical domain (left),and for the associated acoustic pressure in the propagative field (right). Theincompressible terms dominate in the vortical domain. They destructively in-teract in the sum leading to the total radiation. The other striking fact isthe acoustic efficiency of terms 1 and 7, which have an unsignificant sourceamplitude, but a signficant acoustic contribution. Finally, 2nd order acousticsubterms 2 and 3 are negligible, and a destructive interaction is observed be-tween terms 9 and 10, so that these terms have no significant contribution tothe total radiated field.

Fig. 2. Respective amplitudes of the subterms of eq. 2. Left: in the source domain;right: in the acoustic field. In both cases, the value 1 corresponds to the full Lighthillsource term.

A decomposition of the Lighthill source term 5

In a previous study [3], terms 4, 5, 6, 7, 8 were found to be the onlyterms contributing in a temporally evolving mixing layer. In thepresent case, their added contributions, plotted in figure (3-right)do not completely account for the total radiation figure (1-right).Inside this group, terms 4, 6, 8 have a destructive interaction in both vorticaland acoustic domains. In figure 3, it is noted that term 7 radiates downstreamout of phase with respect to the incompressible-driving group radiation.

Fig. 3. Left: contribution of the sum of terms 4, 6 and 8; middle: contribution ofterm 7; right: contribution of the sum of terms 4, 5, 6, 7 and 8.

When the acoustic field produced by term 1 is added to that pro-duced by terms containing kinetic energy and vorticity, the obtained radiationpattern recovers well the emission of the complete Lighthill source term, asseen in figure 4. Term 1 is the product of the momentum vector by the dilata-tion gradient, thus can be viewed as an acoustic quantity transport term. Itscontribution is important in the near field.

Fig. 4. Left: contribution of term 1; right: summed contributions of terms 1, 4, 5,6, 7 and 8.

6 Florent Margnat, Veronique Fortune, Peter Jordan and Yves Gervais

5 Summary - Conclusion

Direct Numerical Simulation, combined with a hybrid prediction method, hasallowed the identification of some important phenomena contained in the non-intuitive expression of Lighthill’s source term. Destructive interference is ob-served between the radiation of the so-called driving terms 4, 6 and 8. Atthe same time, the terms 1 and 7, while weak in the source domain, have ahigh acoustic efficiency, and play a crucial role in the generation of noise thepresent mixing layer, the first one acounting for sound-flow effects, the secondone acounting for compressible response downstream from the vortex pairing.

Acknowledgments

The authors gratefully acknowledge the Agence Nationale de la Recherche(ANR) for financial support, and C. Bogey, C. Bailly & D. Juv at EcoleCentrale de Lyon for helpful discussions.

References

1. Lighthill M. J., On sound generated aerodynamically. I. General theory,Proc. Roy. Soc. A, Vol. 223, pp. 1-32, 1952.

2. Bodony D. J. and Lele S. K. Generation of low frequency sound in tur-bulent jets, 11th AIAA/CEAS Aeroacoustics Conference, Monterey, CA,23-25 May 2005.

3. Cabana M., Fortune V., Jordan P., Identifying the radiating core ofLighthill’s source term, Theoret. Comput. Fluid Dynamics, Vol. 22(2),2008, pp. 87-106.

4. Powell A., Theory of vortex sound, J. Acoust. Soc. Am., Vol. 36(4), 1964,pp. 177-195

5. Howe, M. S., Contributions to the theory of aerodynamic sound, with ap-plications to excess jet noise and the theory of the flute, J. Fluid Mech.,Vol. 71(4), 1975, pp. 625-673

6. Moser C., Lamballais E., Gervais Y., Direct computation of the sound gen-erated by isothermal and non-isothermal mixing layers, 12th AIAA/CEASAeroacoustics Conference, AIAA Paper 2006-2447, Cambridge, Mas-sachussetts, USA, May 2006.

7. Margnat F., Cabana M., Fortune V., Jordan P., Analysis of acousticsource mechanisms in free shear flows, 13th AIAA/CEAS AeroacousticsConference, AIAA Paper 2007-3605, Rome, Italy, May 2007.

Thermal reaction wave simulationusing micro and macro scale interaction model

Andrey Markov , Igor Filimonov, and Karen Martirosyan

Abstract The thermal wave, propagating in a cylindrical tube, is numerically sim-ulated. The technique is developed in order to provide the scale capturing as wellas the stable algorithm for numerical simulation of the combustion wave. Based onthe model kinetics scheme, the fields of temperature, mass fractions, and particleradius are presented for the various values of similarity parameters of the problem.The highly accurate method enables to control scales interaction and justifies variousflow structures. The phase composition, structure, and morphology of the condensedproduct as well as the rate of the oxidation and phase transition are predicted usingthe numerical simulation.

1 Introduction

An increasing number of studies of the synthesis of nanostructured complex oxideshave recently been conducted to support their growing array of emerging technolog-ical applications. A few prominent examples are nanoenergetic materials, advancednanoelectronics, memory devices, digital pigments, biomedical imaging contrast

Andrey MarkovInstitute for Problems in Mechanics of the Russian Academy of Sciences, prosp. Vernadskogo 101,block 1, Moscow, 119526 Russia, e-mail:a−a−markov@yahoo.com

Igor FilimonovInstitute of Structural Macrokinetics and Material Science of the Russian Academy of Sci-ences, Chernogolovka, Moscow Region, 142432, Russia Chernogolovka, Moscow Region, e-mail:f il−limonov@hotmail.com

Karen MartirosyanUniversity of Texas at Brownsville, Department of Physics and Astronomy, 80 Fort Brown,Brownsville, TX, 78520, e-mail:Karen.Martirosyan@utb.edu

1

2 A. Markov, I. Filimonov, and K. Martirosyan

agents, drug delivery and biosensors. Nanoparticles generally have unique novelproperties different from those of bulk materials. Due to their active surface areathey are becoming a core component of advanced materials that have many practicalapplications. The rapidly growing market demand for nanostructured complex ox-ides particulates calls for cost-effective and environmentally friendly technologiesfor their large-scale production. Recently by Martirosyan and Luss [1,2] developed anew, simple, economical and energy efficient synthesis of submicron and nanostruc-tured complex oxides from inexpensive reactant mixtures. In this process, referredto as Carbon Combustion Synthesis of Oxides (CCSO), the exothermic oxidation ofcarbon generates a steep thermal reaction wave (temperature gradient of up to 500C/cm) that propagates at a velocity of 0.1-3 mm/s through the solid reactant mixture(oxides, carbonates or nitrates) converting it to the desired oxide product The re-search of CCSO is only experimental one. The motivation of the present study is todevelop theoretical model of CCSO, using micro and macro scale simulation, how-ever at the moment only condensed two phase flow is considered.The study CCSOfor BaTiO3 kinetics is in progress. The approach by Markov [3,4] is generalized onthermal wave simulation in porous media.

2 Formulation of the problem

Let us consider an arbitrary set ofL simultaneous chemical reactions involvingndistinct chemical species. The bulk and surface reactions are written as follows

n

∑j=1

νv,′i j Cj

kvoli f ,Qvol

i←→kvolib ,−Qvol

i

n

∑j=1

νv,′′i j Cj ;

n

∑j=1

ν′i jCj

ki f ,Qi←→kib,−Qi

n

∑j=1

ν′′i jCj ; i = 1, . . . ,L

Hereνv,′i j , ν

v,′′i j andν

′i j , ν

′′i j are appropriate stoichiometric coefficients forj ’th specie

in the i’th chemical process for bulk and surface reaction respectively. The valueskvol

i f , kvolib are the constant rates for forward and backward bulk reactions andQvol

denote the thermal effect. The valueski f ,kib,Qi are the constant rates and thermaleffects for surface reactions. Let componentsCl , ; l = 1, ...,np change the phasefrom gas to solid due to chemical condensation

Clkl ,ph−→Ql ,ph

Pj ; l = 1, ...,np; np≤ n

Including the phase transition, the mass rate productionMK of specieCK for anarbitrary set ofL simultaneous surface reaction steps is presented in [3].

Let Cj and M j are the mass fraction and molar mass ofj-th specie,ρ is gas

density,Jp j is the rate of condensation of specie,Mvolj is the mass flux for bulk

reaction,csatjb is concentration of saturated vapor of intermediate productCj over

Thermal reaction wave simulation using micro and macro scales 3

particle surface of radiusb, the value ofkphj = k j,ph, j = 1, ...,np andkph

K = 0, j >np.

Using the balance equations of mass and energy, we write down the micro-levelequations for the spherical condensed particle of volumeVb and surface squareSb =4πb2 in a gas volumeV as follows [3].

1Sb

dCjsρsV

dt= M j −M jJp j +β

cj (Cj,ex−Cjs) (1)

Whereβ cj are the mass transfer coefficients.

1Sb

d(CbVbρpTs)dt

= Q+α(Tex−Ts); Q =L

∑i=1

RiQi +np

∑l=1

JplQl ,ph (2)

1Sb

dρpVb

dt= (1− Vb

V)

np

∑l=1

Ml Jpl (3)

Q is the thermal source due to surface reaction,α is the heat transfer coefficient,Cb

is specific heat of particle at constant pressure,ρp is particle density,Vb = 4πb3/3is the particle volume.The subscriptsexandsare referred to values near the particleand at the particle surface. The saturated concentrationcsat

jb with respect toj-speciedepends on critical radiusb j,cr of a condensed particle and on saturated vaporconcentration at plane surfacecsat

j,∞ . These values are found using thermodynamicsconsideration.

The heat transfer and mass transfer coefficientsα andβ cj depend on the coor-

dinates of a particle. These values are found resolving the flow problem near theparticle in the regionb(t) < r < rex [3].

Dρc j

dt= ∇r ·D j (∇rc j) ;

DρCpT

dt= ∇r · (λ∇rT) (4)

r = b(t) : Cj = Cjs; T = Ts; r = rex : Cj = Cj,ex; T = Tex (5)

whereDk is the diffusivity. As the result of solution, we come to the coefficients:

βcj =

D j

(Cj,ex−Cjs)∂Cj

∂ r, α =

λ

(Tex−Ts)∂T∂ r

j = 1, ...,n (6)

The particle is characterized by nondimensional parameterzkb =(

l′0ρ′0

)/(

b′0ρ′b

)where the characteristic values are as follows:l

′0 is the macro scale,ρ

′0 andρ

′b are

the density of gas mixture and solid phase, andb′0 is the particle size.

The Damkoehler numbers are defined as the ratios of time scale for forward,backward chemical reaction and condensation to the time scale for advection trans-port [3]. These scales as well as the Reynolds and Peclet numbers are included inthe coefficients of governing equations.

4 A. Markov, I. Filimonov, and K. Martirosyan

The basic equations are the Navier-Stokes equations supplemented by the termsresulting from microscopic analysis together with relaxation equations for the chem-ical species (see [3] in detail). The governing equations represent the mass conser-vation for gas species, particle number density and size variation, the momentumand energy conservation for carrier gas flow. The flow occurs through a region con-taining fine-scale geometrical structures whose effects, being too small to be numer-ically resolved within the overall calculation, are represented instead as distributedmomentum ’sinks’ or ’resistances’.

∂

∂ t(χρCl )+∇ · (χρuCl ) = ∇ ·

(Pe−1

l χρ ∇Cl)−Jph

l +Jhetl +Jhom

l , l = 1,2, ...n

∂

∂ t(χρ)+∇ · (χρu) =−Jph+Jhet

∂ρb

∂ t+∇ · (ρbu) = Jph−Jhet,

ρb

ρ0b=

nb3

n0b30

∂N∂ t

+∇ · (Nu) = ∇ ·(Pe−1

n ∇N), N = n/n0

∂ (χρu)∂ t

+∇ · (χρuu) = SV −∇p+ Re−1 ∇ · τ

∂ (χρT)∂ t

+∇·(χρuT)= M2A

Dpdt

+M2ARe−1

τ : ∇u+ ∇·(Pe−1

T λ ∇T)+Eph+Ehet+Ehom

Jhet = ∑Jhetl , Jph = ∑Jph

l

Whereχ is the porosity coefficient.The full momentum equations are solved usingthe porous resistance introduced by a (negative) momentum source term in the form:

(SV)i =−uiKi Ki = αi |u| + βi i = 1,2,3

The state equation for perfect gas is used to complete the macro equation set. Ini-tial and boundary conditions are imposed at the entrance of tube and at the wall[3].The subscript zero corresponds to the initial instant. The wall is assumed to bechemically neutral and adiabatic.

3 Computational setup and results of computation

The self-consistent numerical solution of microscopic equations into each cell andmacroscopic equations is applied using the splitting technique [3].

Macroscale resolution. The equations are solved numerically using implicitfinite–difference approximations (see [3] in detail).

Mesoscale resolution. Consider a computational cell which volume isV(x,y,z)and the center is located at a nodex,y,z. Let n(x,y,z)V(x,y,z) be the number of

Thermal reaction wave simulation using micro and macro scales 5

particles uniformly distributed inside the cell andb(t,x,y,z) be the radius of particle.At the 1-st step the heat mass transfer coefficients and the values on the particlesurface are found by solving the system of equations (1-6). At the 2-nd step theaveraged surface mass and thermal fluxesJhet

l ,Jphl are calculated for macroscale

resolution.The results of computation refer to particle number densityn0 = 5 ·1012,zkb =

5 ·102, b0 = 10−6. The reference temperature isT′0 = 1000K and the ignition takes

place at the right sidex = 1 of the tube. Reynolds and Peclet numbers are equal to103 and thermal Peclet number was varied from 10−4 to 1.

The gas and particle parameters, activation energy, and thermal effect are thesame as in [3]. We consider two examples of kinetics as follows:1st type

L = 1,n = 3,np = 1, ν′′11 = 1,ν

′′12 = 0,ν

′′13 = 0,ν

′11 = 0,ν

′12 = 2,ν

′13 = 0

and 2nd type:

L = 2,n= 4,np = 2, ν′′i1 = ν

′′i2 = 1, ν

′′i3 = ν

′′i4 = 0, ν

′i1 = ν

′i2 = 0, ν

′i3 = ν

′i4 = 1, i = 1,2

The results of computation for the 1st type of kinetics are presented in Fig. 1 and 2.Fig. 1. shows the temperature (left) and particle size (right) variation in time.Solid lines and dots correspond to time leveln = 100 andn = 2500 respectively.The results are presented for thermal effect of reactions as followsQ0 = 49,Qs =400,Qph = 1.5. The rate parameters arek0

1 = 109, k02 = 106. Fig. 2 (left) illustrates

the density atn= 100 solid lines andn= 2500 points. We see the spreading of ther-mal wave from right to left and uniform particle growth behind the thermal wave.

At the right side of Fig. 2 the influence of porosity is shown. The particle size ispresented in the region 0< x < 0.8. The dots correspond to the moderate resistanceχ = 0.5, α j = 50, β j = 50, j = 1,2,3 and solid lines are referred to big resistancegiven byχ = 0.05, α j = 500, β j = 500, j = 1,2,3.

The Fig. 3 shows the results for the second type of kinetics and moderate resis-tance of porous media. The influence of Peclet Number is presented via solid linesPeT = 0.01 and dash dot linesPeT = 1.

AcknowledgmentWe wish to acknowledge the support of this research by theNational Science Foundation.

4 References

[1]Martirosyan K.S., and D. Luss, Carbon Combustion Synthesis of Oxides: ProcessDemonstration and Features, AIChE J., 51, 10, 2801-2810, 2005.[2] Martirosyan K.S. , and Luss D. , Carbon Combustion Synthesis of Ferrites: Syn-thesis and Characterization, Ind. Eng. Chem. Res., 46, 1492-1499, 2007. Vol. 46,No. 5, 20, 1492-1499.2007.

6 A. Markov, I. Filimonov, and K. Martirosyan

Fig. 1 The porosityχ = 0.5, α j = 50, β j = 50. The temperature (left) and particle size (right).Solid lines and dots correspond to time leveln = 100 andn = 2500 respectively. The parametersare as followsQ0 = 49,Qs = 400,Qph = 1.5, k0

1 = 109, k02 = 106.

Fig. 2 (Left) The density field variation in time. Solid lines and dots correspond to time leveln =100 andn = 2500 respectively. (Right)The particle size atn = 2500 in the region 0< x < 0.8.Thedots correspond to the moderate resistanceχ = 0.5, α j = 50, β j = 50, j = 1,2,3 and solid linesare referred to big resistance given byχ = 0.05, α j = 500, β j = 500, j = 1,2,3

[3]Markov A. A. Micro and macro scale technique for strongly coupled two-phaseflows simulation. CFD Journal Vol. 16 no.3:28 pp.268-281.2008.[4] Markov, A.A. Multi Scale Numerical Simulation of the Dispersed ReactingFlow, with application to Chemical Vapor Deposition of Alumina. Lecture NotesIn Physics. Proc. 4st ICCFD Ghent,10-14 July 2006. Deconinck, Herman; Dick, E.(Eds.)Vol XX. pp. 753-758, 2009.

Thermal reaction wave simulation using micro and macro scales 7

Fig. 3 The size of particle fractionsb1(left) andb2 (right) at time leveln = 850. for the secondtype of kinetics and moderate resistance of porous media. Solid linesPeT = 0.01 and dash dot linesPeT = 1.

CFD Study on Flow Field inside B.I.P.C. Steam Boilers F. Panahi Zadeh* and M. Farzaneh Gord * Islamic Azad University, Khorramshahr Branch, Khorramshahr, Iran f_panahizadeh@yahoo.com Shahrood University of Technology, Shahrood, Iran imchm@yahoo.co.uk Abstract. The objective of this work is to present a three dimensional CFD modeling for the investigating on the flow field and its nature inside B.I.P.C. steam boilers that are located in Bander Imam petrochemical company, Iran and produced 300 Ton/hr steam for the process purposes. 1 Introduction One of the actions has been done to improve the boilers efficiency is general study of flue gas flow patterns taking place in the boilers. CFD models have proven to be very useful when used as an engineering design tool and as a research and development tool. A significant advantage of computer based simulation over pilot testing is the reduction in the time and capital cost required to investigate design changes. The geometry of studied boiler as shown in figure1 is 9.4×7.7×13 m approximately. The boiler contains six co-firing natural gas and fuel oil burners placed in two stages horizontally separated by 2 m. The first row of the burners is placed at 2.2 m from the boiler bottom and another one has a distance of 9.5 m from the boiler’s roof approximately. The velocity magnitude of inlet air equal 23.86 m/s. The 3D geometry was created using GAMBIT-a FLUENT pre-processor. The whole boiler including: walls, burners, gas duct, etc., was modeled in the real scale. Both the accuracy of a solution and its cost in terms of necessary computer hardware and calculation time are dependent on the grid quality. Hence very care has been taken to generate good quality grid without increasing computational cell inordinately. Figure1 shows the generated grid with 127694 nodes.

Fig. 1. Three-dimensional computational grid for CFD solution

In view of complex flow field in the boiler, this study selects the standard version of k-ε model due to its suitability and robustness for a wide range of wall bound and free-shears flows. The SIMPLEC algorithm is used to couple the pressure and velocity. First order upwind scheme is used to spatial discretization of the convective terms. The solution convergence is obtained by monitoring the continuity, momentum and turbulence separately. A convergence criterion of 10-3 is used for mass conservation and turbulence values.

2 Results and Discussions The velocity vectors of main flow feature are shown in the Figure 2. It can be seen the jet flow exited from burners encounters riser tubes at the end of furnace, turns and causes vortex flow in this area. The vortex flow in furnace improves heat transfer but cause pressure loss. The gas flow towards primary and secondary super heater tubes which located after the furnace. After heat exchange by super heater tubes, the gas enters into riser and down comer tubes zone (zone A). In this zone, a recirculation flow happens in the upper side of water drum and inlet duct. A recirculation flow at this zone cause pressure and heat transfer losses therefore decreases overall efficiency of the boiler.

Fig. 2. Velocity vectors showed by velocity magnitude (m/s)

• The CFD modeling is a useful method to explore the real phenomena, which happens in places that the experimental investigations are impossible or expensive.

• The results provide comprehensive information concerning flow field behavior inside a studied boiler.

• Velocity vectors show a combination of jet flows after burners, which expands inside the furnace and make mixed and circulated areas.

• Flow leaves the furnace through an outlet duct, which is suffering from recirculating flow. This flow variation limited the furnace capacity and increased fuel consumption ratio.

References

[BK86] R.K. Boyd, J. H. Kent, "Three-dimensional furnace computer modeling", Proceedings of Twenty-first Symposium (International) on combustion, the combustion institute, pp.265-274, 1986 [SS9] C.H. Scott, L. D. Smoot,"A Comprehensive three-dimensional model for simulation of combustion systems", PCGC-3, Journal of Energy and Fuels, 7, pp.874-883, 1993 [RKS2006] Masoud Rahimi, Abbas Khoshhal, Seyed Mehdi Shariati," CFD modeling of a boiler’s tubes rupture , Journal of Applied Thermal Engineering,26,pp.2192-2200, Elsevier 2006 [VV2006] R.Vuthaluru, H.B.Vuthaluru ,"Modeling of a wall fired furnace for different operating conditions using Fluent", Journal of Fuel Processing Technology, 87, pp. 663-639, Elsevier 2006