[American Institute of Aeronautics and Astronautics 46th AIAA/ASME/SAE/ASEE Joint Propulsion...

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American Institute of Aeronautics and Astronautics

On The Application of CFD for Cylindrical

Furnace Flow Modeling Eng. Shenoda Tawfik Barsoum

1, Prof.Dr.Karam Ramzy Bishay

2 and Prof.Dr.Essam E. Khalil

2,

1Teaching Assistant

2 Professor of Mechanical Engineering

Faculty of Engineering, Department of Mechanical Power Engineering, Cairo University, Cairo, Egypt,

This paper reports a numerical investigation designed to predict the turbulent flow characteristics in

cylindrical furnace configurations at high Reynolds numbers. In this paper, focus is placed on

numerical predictions technique as a suitable tool to analyze the turbulent flow in different furnace

flow configurations. A commercially available Computational Fluid Dynamics (CFD) simulation

embedded in the FLUENT was utilized. The CFD modeling techniques solved the continuity,

momentum, and energy equations in addition to RNG k–ε modeled equations for turbulence

characteristics. The SIMPLE algorithm is used for the pressure-velocity calculations while

SIMPLEC and a first order upwind scheme were used for discretization of the governing equations.

Mesh sizes used in the present work exceeded 600,000 mesh volumes which allowed better and

meaningful predictions of the flow regimes. Comparisons with the reported experimental data in the

literature were shown and indicated qualitative and trend wise agreements; some discrepancies were

also reported.

I. Introduction

Past and current research activities, reported in the open literature, Khalil

1, Galal2 and Khalil

3-4 had lead to

improved burner and combustion chamber performances with more efficient, stable quite flame, with higher

combustion efficiency has helped to eliminate many parasitic losses and permits the aerodynamic design of

conventional combustion chambers based on numerical computations with reasonable degree of confidence.

Khalil 1 and Khalil

5, reported detailed aerodynamic and combustion characteristics for different furnaces and

burners arrangements as outlined briefly here. The use of asymmetric secondary jets to control the recirculation

zones was reported by AbdelWahab6; the numerical simulation of this aerodynamic stabilization method has

unveiled the three dimensional nature of the flow pattern which possesses a quite large reverse flow region.

The size and strength of the built recirculation zone would be capable of stabilizing the burning of different

fuels including low-quality ones.

On the other hand the application of co-flowing jet with large velocity difference; had been investigated and

indicated the essence of this aerodynamic stabilization method. Also, the effect of burner design principle

invokes the use of two or more small, high-velocity secondary air jets have been studied. The adjusted 3-D

recirculation flow pattern can be used to control the combustion process. In typical power plants, more complex

burner geometries were used in Cairo West steam power plant boiler unit uses nine axial air staged controlled

low NOx oil gas burners. The main problems of these burners are components overheating and meltdown

portions. The study of Khalil 3, extensively investigated the design features of multi-staged industrial burner,

and reported several studies that were devoted to establish the relation between the size and strength of

recirculation zone, the size and shape of obstacles and the intensity of swirl. The basic ideas of numerical

computations of furnace flows have been embodied into the TEACH Computer Program, Gosman et al7.

Previous work of Khalil1, 3

reported extensive survey of modelling of furnace flows.

II. Calculation Procedure

A. Governing Equations The governing equations are those equations governing the fluid motion in space and time. All the fluid

dynamics principles are based upon the following fundamental physical basics:

• Mass is conserved

0=Vdiv ρ (1)

46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit25 - 28 July 2010, Nashville, TN

AIAA 2010-6928

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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• Momentum equations

Dt

Duρ = xgρ

x

P

∂∂

− +

∂

∂+

∂

∂+

∂

∂2

2

2

2

2

2

z

u

y

u

x

uµ (2)

Dt

Dυρ = ygρ

y

P

∂∂

− +

∂

∂+

∂

∂+

∂

∂2

2

2

2

2

2

zyx

υυυµ (3)

Dt

Dwρ = zgρ

z

P

∂∂

− +

∂

∂+

∂

∂+

∂

∂2

2

2

2

2

2

z

w

y

w

x

wµ (4)

• Energy conservation equation is expressed as :

( ) φρ +∇+= TkdivDt

DP

Dt

Dh (5)

when applying these physical principles to a model of the flow; in turn, this application results in equations

which are mathematical statements of the particular physical principles involved, namely, the continuity,

momentum and energy equations

Turbulence Models The present computations made use of the RNG k- ε model due to it’s good predictions of turbulent flow

characteristics under various flow conditions ;Abdel Wahab6. Such model is a variant of the standard k-

ε model and is derived from the instantaneous Navier-Stokes equation using a mathematical technique called

“renormalization group” (RNG) methods .The resulting turbulence model based on that analytical derivation

is different from the standard k- ε model in the value of model constants and some additional terms and forms

appearing in the transport equations for k and ε. For more details about the RNG k- ε model, reference should

be made to Abdel Wahab6. The specifications for the RNG k- ε model are as follows:

Transport Equations

(6)

(7)

Where, Gk, Gb, Sk and Sε are same terms as that of the standard k-ε, while αk and αε are equal to the inverse of

the effective Prandtl numbers for k and ε

Effective Viscosity A differential equation for the turbulent viscosity is obtained from the scale elimination procedure in the

RNG theory.

(8)

Where,

(9)

Where µ is the dynamic viscosity of the fluid.

Equation (8) is integrated to indicate the variation of the effective turbulent transport with

the effective Reynolds number; this would theoretically allow better performance at low

Reynolds number and near wall flows. For the higher Reynolds number region, equation (8)

results in the same equation of turbulent viscosity at case of standard k-ε model. The difference lies in the

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κε

ρε2

2C

value of the constant Cµ = 0.0845, which is derived from the RNG theory, and is very close to the original

empirical value of 0.09

Inverse Effective Prandtl Numbers The RNG theory results in the following formula for calculation of the inverse effective

Prandtl numbers, αk and αε.

(10)

Where α0 = 1.0. In the high Reynolds number region where µmol/µ eff << 1 the inverse effective Prandtl number t

ake value of, αk = αε ≈ 1.393.

Modification of Strain Dependent Term The RNG k- ε model involves an extra term in the transport equation of the turbulent dissipation .The term

Rε which is given by:

(11)

Where,

(12)

This term is to be compared with the term in the ε equation; this takes into account the effects

of rapid strain in complex turbulent flows. i.e., when η < η0 the Rε term is Positive and it adds to the C2ε term

resulting in similar predictions as that of the standard k-ε. But for highly strained flows where η > η0, Rε terms

become negative, and decreases the effective contribution from ρε2/k, thus predicting lower effective

viscosity than the standard k-ε model. The model constants for RNG k-ε model are: C1ε =

1.42, C2ε = 1.68, Cµ = 0.0845. The RNG k-ε model has been shown to result in better predictions than the

standard k- ε model for three dimensional , high Reynolds number flows , but still this model has not been

tested for a wider variety of flows, and has little information available in the literature compared to the

standard k-ε model

The present work made use of FLUENT® 6.2, 8 that was constructed to predict the flow field characteristics

using the standard k-ε model a in the confined enclosures. The present work additionally incorporated the

solution of the energy equation to the computational procedure. These governing equations are solved

sequentially (i.e., segregated from one another). These are non-linear, and coupled, so several iterations of the

solution loop were performed before a converged solution is obtained. The criteria was that normalized

residuals are less than 0.001% .Several grid independency tests were performed to select the adequate grid

arrangement that comprised nearly 600000 nodes.

III. Results and Discussions

In the most heat transfer applications, the existence of highly efficient furnace is of a great importance,

because it will cause some saving in the fuel consumption and enhancement the system performance. This is

related to the mode by which heat is to be transfer. The convection mechanism, especially the natural one, is

always associated with limited heat transfer coefficient value, however with the application of forced

convection in a tube, the heat transfer rate increase, but also up to certain limited values, and the goal of most

designers and researchers is to find out the convenient and possible ways to augment the heat transfer

coefficient.Different techniques were utilized to enhance the heat transfer coefficient in the axial tube. Such

technique raises the turbulence and hence increases the heat transfer coefficient and the frictional losses as well.

One powerful technique is using the swirling flow at the inlet of the tube, and in more cases the swirler is

placed at different position along the tube, in this flow, an additional tangential velocity component is imposed

on the axial distribution. This mechanism increases the contact length between the fluid and tube wall surface

for the same axial length. This mechanism increases the heat transfer rate and the pressure drop. Various swirl

generations were studied by different works.

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In the present works, numerical method is carried out to study the effect of van swirler on heat transfer

enhancement and pressure drop in turbulent tube flow. Two vane swirler are used at the inlet of the tube with

swirl angle 0o and 45

o at different Reynolds number. The flowing air stream is heated, with uniform heat flux,

by an electrical heater wound around the test section of the tube.

Numerical results are compared with the experimental one of Galal 2, these results showing the local heat

transfer coefficient distribution along the tube length, the pressure drop along the tube length and the Nusselt

number, all of this is at different values Reynolds number. The tube in this case study is 1.5 m long and 38 mm

in diameter and wound with an electrical heater to give a uniform heat flux, this tube is insulated from the

outside to ensure that all the heat generated by the electrical heater is totally transfer to the air stream

Figure 1: Measured and Predicted local heat transfer ceofficient at Re=46600 along pipe

Figure 2: Comparisons between Measured and predicted local heat transfer coefficient

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Figure 3: Variation of average heat transfer coefficient with Reynolds number

Figure 4: Relation between the static pressure drop and Reynolds number

Figures 3, 4 indicate the effect of inserting the swirl intensity to the flow at the inlet of the furnace and it’s clear

that the heat transfer coefficient is increased with the inserting the swirl and also the pressure drop are increased

with the insertion of the swirl. More work was reported relating to swirling flow by

Sudden expansion with sudden contraction at furnace exit The design of the furnaces would be greatly facilitated by a procedure for calculating wall heat transfer and

local flow properties as a function of furnace geometry and burner conditions. Such a calculation procedure

would allow the influence of air/fuel ratio, mass flow rates, and burner exit geometry and enclosure dimension

on the distribution of heat flux to be determined; the regions of un-burnt fuel could be located and reduced; and

regions of high temperature and consequent NOx formation could be avoided. Design changes leading to

improve performance could then be made. In this part the sudden expansion furnace is studied to show the

influence of axial and radial velocity for isothermal case, as shown in Figure 5, a 3-D model and the inlet

velocity assumed to be uniform and equal 4.2 m/s. For more details see the work of references 12 and 13.

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Furnace geometry, all dimensions in mm

Figure 5: Flow enclosure and co-axial burner [11]

1 .Axial velocity distributions at Zero Swirl Figure 6 present the influence of the velocity profile on the center line velocity distribution, the annulus mass

velocity is identical and assumed that the velocities are constant in the annulus and central jet. The numerical

profile showed a good agreement with the experimental one.

Figure 6 Center line profile of mean axial velocity, S=0

2. Swirl flow with swirl number = 0.52 In this case of swirl flow with swirl number = 0.52, the jet velocity is zero which mean the jet is off , and this

part studies the effect of swirl on the mean axial velocity profile and also the effect of shutdown the jet flow, as

indicated in Figures 6a,6b and 6 c.

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Figure 6-a Radial profile of mean axial velocity,X/Df=0.067, S=0.52

Figure 6-b Radial profile of mean axial velocity,X/Df=0.17, S=0.52

Figure 6-c Radial profile of mean axial velocity,X/Df=0.34, S=0.52

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The present computational technique was used to numerically predict the furnace flow of Khalil 5; the results

are also compared to the experimental results of reference 5. In Figures 7 at different secondary/primary jet

mass flow rates I.

Figure 7a: Distribution of temperature mixture fraction along the centerline, I=7.1

Figure 7b: Distribution of temperature mixture fraction along the centerline, I=9.7

Figure 7c: Distribution of temperature mixture fraction along the centerline, I=12.65

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It’s clear that the fully developed conditions of the temperature profiles become constant along the axial

direction of the furnace. the numerical results away from the experimental at the beginning of the furnace,

exactly, there is a deviation between the numerical and experimental results from 0.07m to 0.4m downstream

the burner because this area has a more turbulence and high mixture fraction than the other part of the furnace,

and after that distance the results is completely close to the experimental and the mixture fraction become

constant because this area has a low turbulent.Confined jet is of a great importance in combustion application

and the mean different between the free jet and confined jet is the ability of confined jet to create the

recirculation zone, which is necessary to achieve the stability of the flame. In case of confined jet non-premixed

combustion, to accomplish complete combustion the sum of characteristic mixing and chemical reaction time

should be much smaller than residence time. Thus, the mixing enhancement is one of key factors in the

development of such a small combustor satisfying another requirement to secure the flame stability. To

overcome these problems, the forming of a flow recirculation region inside a combustor can be one of the

solutions, which can help the scalar mixing and flame stability.

Turbulent mixing of confined co-axial jets is a complex dynamic process which finds application in a

number of engineering devices such as ejectors, jet pumps, industrial burners, jet engine combustion chambers,

gaseous nuclear rockets, turbofan engine mixing chambers, afterburners, etc. Study of the aerodynamic

behavior of co-axial jets in different types of confinement is also of basic interest because it involves a certain

interacting turbulent flow phenomena. The factors that are involved in a mixing process and are also primarily

responsible for the complexity are: the inlet mass ratio, temperature ratio, density ratio, compressibility and

turbulence levels of the two streams, turbulent swirling flow, and pressure gradient….etc.

Turbulent swirling flows, Non-premixed, are widely used in industrial combustion systems, as indicated

above, for safety and stability reasons. Premixed combustion is well suited to reach very low NOx levels, as

compared with the non-premixed case, but presents a penalty in system complexity; safety and acoustic

instabilities and the use of near-premixed swirl-stabilized combustion in gas turbines may be preferred for

achieving low-NOx emissions.

Swirling motion is regarded as an efficient way to improve and control the mixing rate between fuel and

oxidant streams and to improve flame stabilization through the swirl-induced recirculation of the streams. In

this section, we will study the effect of degree of swirl, showing the effect of input mass ratio on

• Centerline concentration compared with experimental

• Radial concentration compared with experimental

• Velocity and stream lines contours

• Velocity profiles

• Comparing all the above for different inlet mass flow rate of secondary streams

Figure.8a, 8b,8c show the corresponding distributions of temperature mixture fraction along

the centerline at different inlet conditions with secondary inlet mass flow rate ms=405 Kg/hr comparing the

numerical results with the experimental results of Khalil5.

Figure 8a: Distribution of temperature mixture fraction along the centerline, I=5.21

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Figure 8b: Distribution of temperature mixture fraction along the centerline, I=7.1

Figure 8c: Distribution of temperature mixture fraction along the centerline, I=9.7

Figure 8d: Distribution of temperature mixture fraction along the centerline, I=12.65

It’s also the same conclusion which taken from zero degree of swirl and it’s clear that the fully developed

conditions of the temperature profiles become constant along the axial direction of the furnace, the numerical

results away from the experimental at the beginning of the furnace. The numerical results of zero degree of

swirl are too close to the experimental results, but for 45o the deviation between the numerical and experimental

results is clear and too much than the deviation in zero swirl especially at the inlet of the burner.

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Comparison between stream lines for all inlet conditions: Using swirl flow in secondary air stream for isothermal flow in confined jet is of a great

importance in combustion application to increase the ability to create the recirculation zone, which is necessary

to achieve the stability of the flame.

Fig 9-a,b ,c , d representing the contour of mixture stream lines and shows the effect swirling

the secondary flow and changing the inlet mass ratio of the two air streams on the wall recirculation zone, it’s

clear that the swirling flow increase the recirculation zone than zero swirl and as the inlet mass ratio increase,

i.e decreasing the primary inlet velocity, the wall recirculation zone is decrease with a small value, so, we can

notes that the ratio of secondary and primary streams has a small effect on the size and length of the

recirculation zone except for the input mass ratio 5.21, but for the input mass ratio 12.65 the mixing between the

two streams

Figure 9-a: Contour of mixture stream lines Kg/s, X-Y plane, X=5.21

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Figure 9-b: Contour of mixture stream lines Kg/s, X-Y plane, I=7.1

Figure 9-c: Contour of mixture stream lines Kg/s, X-Y plane, I=9.7

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Figure 9-d: Contour of mixture stream lines Kg/s, X-Y plane, I=12.65

Figure 10-a, b, c, d representing the contour of mixture axial velocity and showed that the

axial velocity is clearly positive in the direction of the flow at the zone around the centerline of the furnace but

the reverse flow happens at the zone near to the wall of the furnace approximately till 0.1 m just downstream

the furnace for the four above inlet conditions, and the flow is developed symmetrically around the furnace axis,

and it’s clear that as the inlet mass ratio increase, i.e decreasing the primary inlet velocity, decreasing the

Reynolds number, the recirculation zone is decrease and the minimum axial velocity in the recirculation zone is

also decrease

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Figure 10-a: Contour of mixture axial velocity m/s, X-Y plane, I=5.21

Figure 10-b: Contour of mixture axial velocity m/s, X-Y plane, I=7.1

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Figure 10-c: Contour of mixture axial velocity m/s, X-Y plane, I=9.7

Figure 10-d: Contour of mixture axial velocity m/s, X-Y plane, I=12.65

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IV. Concluding Remarks

This paper introduces a well developed Computational Fluid Dynamics (CFD) program to predict the airflow

and flame characteristics in the furnaces, based on two equation turbulence model. The spatial nature of the

flow characteristics is described and explained in the present work. It is observed that the numerical results

have qualitative agreement with the previous experimental and numerical results. The present program should

be subjected to further development in future to extend its capabilities to more adequately describe the

combustion-time processes and turbulence-chemistry interactions .The final goal is to support the engineers

and designers of the furnaces and combustors.

References 1. Khalil, E. E. 1983 "modeling of furnaces and combustors". Abacus Press, 1 st Edition, U.K.

2. Galal. M. Mostafa,1993, “Optimization of using vane swirling to augment heat transfer in turbulent in

turbulent swirling tube flow”-1993

3. Khalil. E. E . 1978, Numerical Procedures as a tool to Engineering Design, Proc. Informatica 78,

Yugoslavia.

4. Khalil, E. E., 1980 “Initial and boundary conditions and their influence on numerical computations of

confined elliptic flows” Faculty of Engineering, Cairo University, 1980.

5. Khalil ,A.K.H.,1974 “Theoretical and experimental investigation of the mixing process of a gas stream

and swirling air stream with special reference to the fuel-air mixing ”-MSc, Cairo University, 1974

6. AbdelWahab, A., 2008. “Numerical investigation of mixing process of primary and secondary air

stream in furnace under non-reacting conditions”, M.Sc, Cairo university, 2008

7. Gosman, A. D., Pun, W. M., Runchal, A. K., Spalding, D. B., and Wolfstien, M. 1969 "Heat and Mass

transfer in Recirculating flows" (Academic press.).

8. Fluent Inc,2005

9. Baker, R. J. , Khalil E,E. and Whitelaw,J.H.,1974, “the calculation of the furnace-flow properties and

their experimental verification”, Imperial College, London, England-1974

10. Khalil ,E.E. and Whitelaw,J.H.,1974 “the calculation of the furnace-flow properties and their

experimental verification”, Imperial College, London, England-1974

11. Khalil, E. E., 1977 "Flow combustion & heat transfer in axisymmetric furnaces" Ph.D. Thesis, London

University.

12. Khalil, E. E., Spalding, D. B., and White law, J. H. 1975 "The calculation of local flow properties in

two dimensional furnaces" Int. 1. Heat and Mass Transfer, 18, page 775.

13. Launder, B. E., and Spalding, D. B., "Mathematical Models of Turbulence", Academic press,London,

1972

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