Evaluation of gas radiation models in CFD modeling of oxy-combustion

Energy Conversion and Management 81 (2014) 83–97

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Evaluation of gas radiation models in CFD modeling of oxy-combustion M.A. Rajhi a, R. Ben-Mansour a, M.A. Habib a, M.A. Nemitallah a,b,⇑, K. Andersson c a

Mechanical Engineering Departments, KFUPM, Dhahran 31261, Saudi Arabia Mechanical Engineering Department, Massachusetts Institute of Technology, 77 Mass Avenue, Cambridge, USA c Department of Energy and Environment, Energy Technology, Chalmers University of Technology, SE-412 96 Goteborg, Sweden b

a r t i c l e

i n f o

Article history: Received 4 October 2013 Accepted 7 February 2014 Available online 3 March 2014 Keywords: Gas radiation models Oxy-fuel combustion Air combustion Computational fluid dynamics (CFD)

a b s t r a c t Proper determination of the radiation energy is very important for proper predictions of the combustion characteristics inside combustion devices using CFD modeling. For this purpose, different gas radiation models were developed and applied in the present work. These radiation models vary in their accuracy and complexity according to the application. In this work, a CFD model for a typical industrial water tube boiler was developed, considering three different combustion environments. The combustion environments are air–fuel combustion (21% O2 and 79% N2), oxy-fuel combustion (21% O2 and 79% CO2) and oxy-fuel combustion (27% O2 and 73% CO2). Simple grey gas (SGG), exponential wide band model (EWBM), Leckner, Perry and weighted sum of grey gases (WSGG) radiation models were examined and their influences on the combustion characteristics were evaluated. Among those radiation models, the EWBM was found to provide close results to the experimental data for the present boiler combustion application. The oxy-fuel combustion characteristics were analyzed and compared with those of air–fuel combustion. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Energy production from fossil fuel combustion results in the emission of carbon dioxide (CO2) and nitrogen oxides (NOx). Reduction of these pollutants becomes an international community interest and many investigators have been adopted for this purpose. One of the most promising options to capture carbon dioxide (CO2) and reduce NOx emission is oxy-fuel combustion in which the combustion utilizes pure oxygen instead of air. Thermal radiation is the principal mode of heat transfer in the combustion chamber and the radiative properties of combustion products such as CO2 and H2O affect the heat transfer to the furnace wall tubes. In the present work, the transfer of radiant energy was obtained from the solution of the radiative transfer equation (RTE) as described in the coming sections. The radiative transfer equation is of the integral–differential type. This equation is complex and, therefore, it is difficult to be exactly solved in 3-D geometries. The following simplifications to this equation were, therefore, incorporated. Since the scattering in the combustion of gas fuel (such as Natural Gas, CH4 and Propane, C3H8) has an insignificant ⇑ Corresponding author at: Mechanical Engineering Department, Massachusetts Institute of Technology, 77 Mass Avenue, Cambridge, USA. Tel.: +966 598212483. E-mail addresses: [email protected], [email protected] (M.A. Nemitallah). http://dx.doi.org/10.1016/j.enconman.2014.02.019 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.

effect, it can be neglected in the RTE. By applying this simplification, the radiative transfer equation becomes a differential equation, which is much easier to be solved than the integral– differential equation. Viskanta [1] indicated that, in cases where soot particles are small, such as those cases of methane and propane combustion, the scattering is a function of the soot particle diameter raised to the power four. Accordingly, it is justified to neglect the scattering effect in the present calculations. However, this assumption cannot be generalized to other combustion applications. Thus, care should be taken during the treatment of the soot modeling as it directly affects the radiation heat transfer. Soot particle size effects on the radiation heat transfer were reported in many studies for different combustion applications [2–4] and different flame types [5,6]. The generation rate of soot particles inside many combustion applications has been described in various models. Those models have shown good agreement with experimental data for different flame types and different combustion applications [7]. The influence of soot particles on the radiation heat transfer in a multi compartment system has been demonstrated by Yeoh et al. [8]. Their numerical results have shown good agreement when compared with the experimental data of Luo and Beck [9], considering the soot model proposed by Moss et al. [10] and Syed et al. [11]. Yeoh et al. [8] concluded that the accurate calculation of the rate of soot generation is very essential for accurate CFD modeling of combustion.

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Nomenclature Iv I Ib Ib,m L c Ak

Pe X PE ae,i be,i,j aa,i ca,i,j,k Eov C;k

spectral radiation intensity (W m2 sr1 Hz1) total intensity (W m2 sr1) blackbody intensity (W m2 sr1) spectral black body intensity (W m2 sr1 Hz1) path length (m) velocity of radiation (m/s) total band absorptance of band k (Hz if frequency is used in the integration, lm if wavelength is used, cm1 if wavenumber is used) equivalent broadening pressure density path-length (g/m2) effective pressure (bar) emissivity weighting factors for the grey gas i emissivity gas temperature polynomial coefficients absorptivity weighting factors absorptivity polynomial coefficients spectral blackbody emissive power (W/(m2 Hz), or other units if wavelength or wavenumber is used)

Greek symbols b mean line-width-to-spacing parameter e emissivity ec emissivity of carbon dioxide eg total gas emissivity ew emissivity of water vapour ek spectral emissivity f partial pressure ratio g pressure corrected line-width-to-spacing parameter k stoichiometric ratio kmax pressure correction parameter

The Soot generation rate should be accurately predicted in the flame zone in order to correctly predict the combustion characteristics inside any combustion system, especially for the case of oxyfuel combustion [12]. Changing the energy carrying medium from nitrogen in case of conventional air combustion to carbon dioxide in case of oxy-fuel combustion is expected to result in modifications in the soot generation rate [13]. It has been confirmed, in many recent publications, that oxy-fuel combustion results in less amount of soot [14,15]. Predictions of nine total emissivity models against the calculations conducted using the EWBM were compared by Lallemant et al. [16]. Hottel et al. [17] showed that the thermal radiation from water vapour, carbon dioxide, fly ash, soot and carbon monoxide presents the major contributor of heat transfer from a flame produced by conventional fuels. Any change of CO2 and H2O concentrations results in a change in radiative heat transfer. For air combustion with conventional partial pressures of CO2 and H2O, the heat transfer calculations are carried out by using a three grey-one clear gas model to estimate flame emissivity. The concentrations of CO2 and H2O gases in oxy-fuel combustion are high in comparison to those of air-fired combustion. Both CO2 and H2O, unlike N2 which is transparent to thermal radiation, emit and absorb thermal radiation. Accordingly, the emissivity of the flue gas increase in the case of oxy-fuel combustion due to the high concentrations of absorbing/emitting gases. These have subsequent effects on the radiative heat transfer. Wall [18] stated that the heat transfer prediction is critical to oxy-fuel technology, since there are changes in gas properties due to CO2 recycling from furnace outlet back to the furnace inlet. These changes are attributed to alteration of gas radiative properties and gas heat capacity.

r s sH sk sk,i?n x eo jv rv Uv

a x Dec+w g, l, n

Stefan Boltzmann constant (W m2 K4) transmissivity optical depth at band head transmissivity of band k transmissivity of band k and path i ? n bandwidth parameter (cm1) zero partial pressure emissivity spectral absorption coefficient scattering coefficient phase function integrated band intensity (cm1/(g/m2)) band width parameter (cm1) overlap between bands of CO2 and H2O direction cosine

Abbreviations DOM discrete ordinates method RTE radiative transfer equation LBL line-by-line model SNB statistical narrow band model WBM wide band model CFD computational fluid dynamics WSGG weighted sum of grey gases model EWBM exponential wide band model SLW spectral line-based weighted-sum-of-grey-gases model SGG simple grey gas model BA block approximation method BEA band energy approximation

During oxy-fuel combustion, the flue gas tri-atomic molecules concentration increases drastically and this leads to changes in the gas emissivity. In order to assess the suitability of retrofitting an air-fired boiler to oxy-fuel combustion, Zheng et al. [19,20] calculated the gas emissivity from the correlations suggested by Leckner [21] for total gas emissivity for the water vapour and carbon dioxide. Andersson and Johansson [22] studied experimentally the combustion of propane fuel for three test cases: air–fuel combustion (referenced one) and other two oxy-combustion cases (OF21 @ 21% O2 and OF27 @ 27% O2). The difference in total radiation intensity between these cases was determined and compared. In addition, the difference in combustion environment was described. They reported that, in case of the OF 21 combustion, the temperature levels were found to be lower than those of air-fired condition. This was attributed to two reasons; (1) the higher specific heat capacity of CO2 compared to N2, and (2) increase in radiation losses caused by the CO2 with increase the gas emissivity. In a recent study, Johansson et al. [23] evaluated several approximate gas radiative property models for oxy-fuel environments in large atmospheric boiler. These models included statistical narrow band (SNB) models, WSGG model, spectral line-based weighted-sum-ofgrey-gases model (SLW) and two grey-gas approximations model. The accuracy of the radiation models is determined by the importance of the radiative source term. Lallemant et al. [16] indicated that the heat released by combustion dominates the radiative release in regions of intensive combustion. They compared gas radiation models with measurements of total radiation intensity in a 300 kW non-sooting natural-gas flame. The agreement between measurements and computed data by the EWBM was

M.A. Rajhi et al. / Energy Conversion and Management 81 (2014) 83–97

excellent for measurements against cold furnace walls. The WSGG model is recommended when the influence of the radiative source term is significant. Porter et al. [24] used the spherical harmonic (P1) and the discrete ordinates method (DO) to solve the RTE in multi-dimensional problem. The spectral nature of radiation has been treated by using non-grey gas full spectrum k-distribution method (FSCK) and a grey method. The simulation results of air– fuel and oxy-fuel combustion were compared with the statistical narrow band model (SNB). They concluded that the non-grey full spectrum k-distribution method was in good agreement with the statistical narrow band model (SNB). Significant errors were introduced in the wall heat flux when a grey model was used. The WSGG model is based on the fitting of air–fuel combustion characteristics. This model was modified by Johansson et al. [25] to become suitable to cover the temperature range of 500–2500 K in order to be used in case of cover oxy-fuel combustion. They have reported that the modified WSGG is a computationally efficient option for CFD simulations. Hjärtstam et al. [26] utilized the CFD method to investigate the influence of gas and gas-soot radiation mechanisms in air and oxy-fuel flames when propane fuel is burnt in a 100 kW test furnace. They showed that in the case of Oxy-fuel combustion both grey and non-grey weighted sum of grey gases models overestimate the peak temperature. In addition, they stated that, the inclusion of soot modeling in both grey and non-grey gas radiation models has a significant impact in the CFD calculations. In the present work, a CFD model was developed and used to simulate three different combustion environments based on different gas radiation models. 2. Gas radiation models In the present study, the radiant energy was calculated from the RTE solution. This equation is based on the conservation principle applied to a monochromatic bundle of radiation. The RTE is given by Viskanta [1] as follows:

1 dIv rm ¼ ðjv þ rv ÞIv þ jv n2v Ibv þ c dt 4p ! mÞIv 0 ð~ s0 ÞdX0 dm0

Z Dm;

Z X¼4p

Um ð~ s0 ! ~ s; m0

spectral transmissivity averaged over a narrow band. This model is suitable for the radiation heat transfer prediction in high temperature mediums. The wide band model (WBM) is a simplification of the SNB model; it yields wide band absorptance and requires the knowledge of the path length in the model as well as the spectral parameters associated with the path length. In the following subsections, the details of the considered gas radiation models in the present work are presented. 2.1. Simple grey gas model (SGG) The simple grey gas model (SGG), in addition to being simple, it requires low execution time. The model considers the effective absorption coefficient as the main parameter controlling the radiative properties of a gas mixture and assumes that radiant absorption and emission by gas molecules to be independent of the frequency of the radiation. Under the grey gas assumption, and neglecting scattering of radiation, the RTE for the radiation intensity (integrated over the entire spectrum) in 3-D Cartesian coordinates is expressed as follows:

n

@I @I @I þ g þ l ¼ je I þ je Ib @x @y @z

where the different coefficients and terms of the above equation are defined as: ‘‘Iv’’ is the spectral radiation intensity, ‘‘c’’ is the speed of electromagnetic wave in vacuum, ‘‘jv’’ is the spectral absorption coefficient, ‘‘rv’’ is the scattering coefficient, ‘‘Ibv’’ is the Planck’s spectral blackbody intensity of radiation, ‘‘nv’’ is the spectral index of refraction of the medium and ‘‘Uv’’ is the phase function. The spectral radiation intensity is a function of three spatial coordinates, time and two angles, in addition to the radiation frequency or the wavelength. Solution of radiative transfer requires models to account for the directional and spectral natures of radiation. One of the popular methods to treat the directional nature of radiation is the discrete ordinates method (DO). The method is originally suggested by Chandrasekhar [27] for astrophysical applications. This method was applied in the present calculations and its solution was obtained through the solution of Eq. (1) for a set of discrete directions spanning the total solid angle range of 4p. The spectral nature of radiation is very important aspect in the gas radiation treatment. In general, there are three different models used to define the radiative properties of combustion gases [28]. Those models are the Spectral line-by-line models, the Spectral band models and the Global model. The complexity of the models decreases from the line model to the global model. In the line-by-line (LBL) model, the RTE is integrated over detailed molecular spectrum for the gases. This model is used only for benchmark solutions due to the enormous amount of computational requirements. The statistical narrow band model (SNB) provides the

ð2Þ

In the full modeling of a gas-fired furnace, the RTE is solved for known temperature field and species concentration that are determined by conservations equations of motion, energy and mass of species. At the start of the solution, an initial guess is made for all of the parameters. Then, iterative methodology is used in order to get the final converged solution. The RTE is solved based on the calculations of temperature and species concentrations from the previous step. A good estimation of the effective absorption coefficient from the known properties (a mean beam length Lm and a characteristic gas temperature) of emission by the gas can be obtained from interpretation of the total emissivity of the gas upon the bounding surface. The characteristic temperature can be the volume–average gas temperature Tm, as given in the following equation:

je ¼ ð1=Lm ÞIn½1  eg ðT m ; Lm Þ ð1Þ

85

ð3Þ

Or the local temperature, T, giving a locally varying value,

je ¼ ð1=Lm ÞIn½1  eg ðT; Lm Þ

ð4Þ

The mean beam length is estimated as

Lm ¼ 3:6V=S

ð5Þ

where V represents volume of furnace and S is the wall surface area. 2.2. Exponential wide band model (EWBM) The exponential wide band model is based on a physical analysis of gas absorption. This model provides a set of semi-empirical expressions to predict the total band absorptance of infrared active molecules. This model can be used to predict radiative properties in a wide range of temperature, total pressure range, volumetric fraction and path length [29]. In this model, it is assumed that the total absorption of a vibration–rotation band can be approximated with correlations dependent on three parameters: the integrated band intensity, a, the band width parameter, x, and the mean line-width-to-spacing parameter, b. These parameters depend on temperature, but pressure effects are also accounted for through the equivalent broadening pressure, Pe. The parameters yield asymptotic relations for the total band absorptance Ak. These relations are known as the four-region expression, which is defined as linear, square root, log-root and logarithmic regions. The expressions of the band transmissivity, sk, are derived from the relation:

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sk ¼

sH @Ak Ak @ sH

ð6Þ

The optical depth at the band head sH and the pressure correction parameter g are calculated from:

aX x

ð7Þ

g ¼ bPe

ð8Þ

sH ¼

where X is the density path-length. The parameters a and b are calculated according to the simplified relations presented by Lallemant and Weber [29], while x is given by a correlation dependent on temperature. In order to calculate the total emissivity of H2O–CO2 mixtures, band energy approximation (BEA) is used. In this method, it is assumed that the blackbody emissive power is constant over each absorption band. The total emissivity is given by the following equation [30]:

eg ffi

o k¼N E X v C;k  Ak  Decþw r  T4 k¼1

2.3. Leckner model The model was developed by Leckner in 1972 [21]. The CO2 and H2O emissivities are treated separately. Then, the total emissivity of the mixture is determined by taking a total band overlap correction term into consideration. The advantage of this model is that it can be applied for any arbitrary partial pressures of CO2 and H2O. The total emissivity for a mixture of CO2 and H2O is calculated from the following equation:

ð10Þ

In this model, a zero partial pressure emissivity for either CO2 or H2O is given by:

ln eo ¼ ao þ

i¼M X

i

ai k

ð16Þ

  p PE ¼ PT 1 þ 0:28 c pT

ð17Þ

The total emissivity of the gas mixture of H2O and CO2 for the desired partial and total pressures is equal to the sum of emissivities of the two gases minus a correction term Decw due to overlap in some spectral regions. The overlap between the two gases is approximated by the following equation:

Decw ¼



f  0:0089f10:4 10:7 þ 101f



 k2:76

ð18Þ

In which the partial pressure ratio f is given by

f¼

pw pw þ pc

ð19Þ

and the parameter k is defined as

ð9Þ

The correction term, Dec+w, accounts for the overlap between the 2.7 and 15 lm bands for mixtures of CO2 and H2O. The simplified procedure proposed by Modak [31] is used in the present study to calculate this overlapping.

eg ¼ ec þ ew  Decw

  p pffiffiffiffiffiffiffiffiffiffiffiffiffiffi PE ¼ PT 1 þ 4:9 w 273=T pT

ð11Þ

i¼1

k ¼ log10 ððpw þ pc Þ  LÞ

ð20Þ

2.4. Perry model Empirical correlations for the emissivities of water vapour, carbon dioxide, and four mixtures of the two gases were developed in the 8th edition of the Perry’s Chemical Engineering Handbook [32]. They are valid to be used for pressure-path-length of range .005– 10 m-atm. The emissivities at three temperatures of 1000, 1500 and 2000 K at six values of partial pressure ratios of H2O/CO2, namely, 0, 0.5, 1.0, 2.0, 3.0 and 1 can be calculated by Eq. (21). Empirical constants for different partial pressure ratios of H2O/ CO2 are given in [32]. These correlations were developed based on the data in Hottel emissivity charts [17] and were adjusted to the more recent data from cross-handler [33]. Linear interpolation or extrapolation of the emissivities determined at 1000, 1500 and 2000 K is used in order to obtain the emissivity at different temperature and it is given by the following equation:

eg T g ¼

eg T H ðT g  T L Þ þ eg T L ðT H  T g Þ 500

ð21Þ

where TH and TL are the higher and the lower temperature, respectively.

In which: 2.5. Weighted sum of grey gas model (WSGG)

j¼N X ai ¼ C oi þ C ji sj

ð12Þ

j¼1

k ¼ log 10ðpi LÞ

ð13Þ

where pi L is the pressure path length of either H2O or CO2 (given in bar.cm) and s = T/1000 (the gas temperature T is given in K). The coefficients Cji are found in Ref. [21]. The pressure correction term is determined using the relation:



ei 1 eo



ei 1 eo



¼ expfnðkmax  kÞ2 g

ð14Þ

max

where ei is the emissivity of either CO2 or H2O. At high pressures the emissivity follows an asymptotic behavior according to:

 

ei eo

¼ max

A  PE þ B PE þ A þ B  1

ð15Þ

The parameters n, kmax, A and B are given in Ref. [21]. The effective pressure PE is defined in Eqs. (16) and (17) for H2O and CO2 respectively.

There are several gas radiative properties models, called global models; they are based on the concept of weighted sum of grey gases. Example of these models is Hottel and Sarofim’s gas radiative properties model [17]. Eq. (22) is used for the evaluation of total emissivity in terms of the weighted sum of grey gases and it is useful especially for the zonal method of analysis of radiative transfer.

e¼

i¼I X ae;i ðTÞ½1  eji PL 

ð22Þ

i¼0

where ae,i is the emissivity weighting factors for the grey gas i. The weighting factors are dependent on gas temperature T. ji, is the absorption coefficient, P is the sum of partial pressures of absorbing gases and L is the thickness of gas layer, or path length. The weighting factor for clear gas, i.e. for i = 0, is defined as:

ae;0 ðTÞ ¼ 1 

i¼I X ae;i i¼1

ð23Þ

M.A. Rajhi et al. / Energy Conversion and Management 81 (2014) 83–97

87

A common representation of the temperature dependency of the weighting factors is a polynomial of order J  1 given as:

ae;i ðTÞ ¼

j¼J X be;i;j T j1

ð24Þ

j¼1

where be,i,j is referred to as the emissivity gas temperature polynomial coefficients. The absorption coefficients ji and the polynomial coefficients be,i,j are obtained by fitting Eq. (22) to a table of total emissivities previously calculated from the EWBM. The total emissivities for various gas mixtures can be obtained utilizing experimental measurements, by calculation based on spectral lines or bands based on Hottel’s charts, etc. The total absorptivity is calculated as follows:

a¼

i¼I X aa;i ðT; T s Þ½1  eji PL 

ð25Þ

i¼1

where aa,i is the absorptivity weighting factor, T is the gas temperature and Ts is the surface irradiation temperature. The weighting factors for a CO2/H2O/clear gas mixture with PCO2 = 0.1P, PH2O = 0.2P, and P = 101.3 kPa, have been reported by Truelove [34]. All the WSGG model parameters, i.e. weighting factors and absorption coefficients, are intended for air-combustion conditions, and their validity to be used in oxy-fuel combustion is limited. Pressure path-lengths and ratios of H2O to CO2 in oxy-fuel combustion are drastically different from that of conventional combustion. Therefore, there is a need to derive new parameters to be used in these models. Johansson et al. [23] have developed two WSGG models, the first consist of three grey one clear gas, and the second of four grey one clear gas.

Fig. 1. Layout of the furnace of the present boiler.

excessive air). It is assumed that all fuel is converted to combustion products of CO2 and H2O and the total heat input into the furnace is 295 MW. The fuel mass flow rate through each burner is about 0.98 kg/s. Primary and secondary air passing through each burner are equal to 8.87 kg/s and 10.7 kg/s respectively. The combustion process takes place in environment of atmospheric pressure. The volume of the furnace was discretized into 1,335,180 control volumes. This analysis covers three different combustion environments; (1) AF21 (21% O2 and 79% N2), (2) OF21 (21% O2 and 79% CO2) and (3) OF27 (27% O2 and 73% CO2).

3. Boiler description and CFD modeling 3.2. CFD modeling 3.1. Boiler description CFD modeling of a full scale fossil-fuel fired furnace is conducted in this study. The objective of this modeling is to investigate the influence of radiation models on combustion characteristics and to analyze the impact of replacing air with a mixture of O2– CO2 in the combustion. The boiler is manufactured by Mitsubishi Heavy Industries (MHI) and is operated in Saudi Aramco refineries. A brief summary of design data is given in Table 1. The layout of this boiler is depicted in Fig. 1. It consists of D-type tubes that extend from the mud drum (lower drum) through the bottom wall, the side wall, top of furnace and ends at the upper drum. The tubes forming the bottom wall are thermally insulated. Tubes on the front wall extend from lower to upper drum while the tubes forming the side walls extend from a lower header to an upper header. The water-steam mixture inside the tube is, under steady state conditions, normally saturated having a saturation temperature corresponding to the drum pressure. Accordingly, the furnace walls provide a constant temperature (538.6 K) boundary condition. As shown in Fig. 1, the boiler consists of 6 burners located in two levels. Each burner has eight fuel nozzles with 24 fuel jets in each nozzle. The burner construction is shown in Fig. 2. Methane fuel (CH4) is burnt in the furnace with stoichiometric ratio of about 1.16 (16%

Table 1 Design data of the boiler. Mass flow rate of steam, lb/h

Drum pressure, psig

Steam temperature, F

Number of burners

750,000

750

750

6 on two levels

The set of governing differential equations, i.e. continuity, momentum, energy and conservation of chemical species, together with the boundary conditions were numerically solved. The steady-state mass, momentum, energy and species conservation equations for Newtonian fluids were considered:

r  ðqUÞ ¼ 0

ð26Þ

r  ðqUUÞ ¼ rP þ lr2 U

ð27Þ

ðqC P ÞU  rT ¼ r  ðkrTÞ

ð28Þ

r  ðqUY i Þ  r  ðqDi rY i Þ ¼ 0

ð29Þ

where u is the velocity vector, q is the fluid density, p is the pressure, l is the dynamic viscosity, k is the thermal conductivity, Di is the diffusion coefficient, and Yi is the scalar species mass fraction. The CFD Fluent package [35] utilizing the finite volume method is used for representing and evaluating partial differential equations in the form of algebraic equations. The CFD calculations normally provide detailed results including velocity, temperature, species concentrations and heat flux that are not easily obtained through experimental measurements. The models that used in the solution are [36–40]; (1) Incompressible ideal gas assumption, (2) Standard k–e turbulent model, (3) Temperature-dependent properties, (4) Two-step oxy-combustion volumetric reactions for species transport, (5) Finite-rate/Eddy-dissipation turbulence-chemistry interaction, and (6) Discrete Ordinate Radiation Model (DO). The discretization of the governing equations was conducted through the use of a segregated solver (each equation is solved separately. In order to couple the calculations of pressure and velocity, a Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)

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Fig. 2. The burner construction.

Table 2 Modified two-step methane–oxygen combustion mechanisms with kinetic rate data [41]. Reaction number

Reactions

A

b

Ea (J/kmole)

Reaction orders

Reaction 1 Reaction 2 Reaction 3

CH4 + 1.5O2 ? CO + 2H2O CO + 0.5O2 ? CO2 CO2 ? CO + 0.5O2

1.59  1013 3.98  108 6.16  1013

0 0 0.97

1.998  108 4.18  107 3.277  108

[CH4]0.7[O2]0.8 [CO][O2]0.25[H2O]0.5 [CO2][H2O]0.5[O2]0.25

Table 3 Different grids for furnace modeling.

1 2 3

Grid name

Number of cells

Percentage of increasing

Grid-1 Grid-2 Grid-3

935,805 1,095,555 1,335,180

– +17 +43

2000 1800

Grid-1 Grid-2 Grid-3

1600

Temperature (K)

scheme was applied. The solution was converged when the summation of the residual in the governing equation at all the domain nodes was less than 0.01%. The ideal gas law was used to determine the gas density and the pressure staggered scheme (PRESTO) was applied. Thermal conductivity, viscosity, and specific heat of the gas were determined as a mass fraction-weighted average of all the species. For each species, the specific heat was determined through the application of a temperature piecewise polynomial fit. To obtain more accurate results, the second-order upwind discretization scheme was applied for the solution of momentum, species and energy equations. A constant temperature boundary condition was applied to all furnace walls, 538.6 K, and the combustion is conducted under atmospheric conditions. Methane (CH4) was used as the operating fuel with a rate of 0.98 kg/s and an excess air factor of 1.16% was applied during the combustion process. For each burner, the primary and secondary air flows were set to 8.87 kg/s and 10.7 kg/s, respectively. The solution of the RTE cannot be obtained unless the absorption coefficient is known. It can be determined from the computed emissivity at each computational cell by employing the Beer–Lambert’s law and taking the mean beam length of the geometry as the path length. SGG model, WSGG model, the EWBM, Leckner model and Perry model are applied in the solution. They are coded and compiled as User-defined functions (UDFs). Among these models, the EWBM provided close results to the experimental data for the present boiler combustion application. The standard k–e model is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (e). The model transport equation for k is derived from the exact equation, while the model transport equation for e was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart. On the other hand, for the realizable model, the term ‘‘realizable’’ means that the model satisfies certain mathematical constraints on the normal stresses. The RNG model accounts for the flow curvature and considers additional terms for

1400 1200 1000 800 600 400 200

0

1

2

3

4

5

6

7

Distance along Z-axis (m) Fig. 3. Temperature profile at line (x = 4.539, y = 2.135) along Z-axis.

wall treatment. However, in the present combustion modeling, the most important zone is the close region to the burner not that zone close to the wall. Based on accurate calculations of the turbulence interaction and the reaction rates in this zone, the whole combustion characteristics can be properly calculated. Based on that, the standard k–e model was applied in all of the present calculations.

M.A. Rajhi et al. / Energy Conversion and Management 81 (2014) 83–97

-6.0E+04 -8.0E+04

Total Heat Flux (W/m2)

present work for the calculations of the reaction kinetics. The model was modified to handle the increased CO2 concentration under oxy-fuel conditions. The two step reaction kinetics model has been considered in this work for simplification of the reactions kinetics calculations with reasonable results regarding the species concentrations as compared to the detailed model [41]. For this model, the modified reactions rates data by Andersen et al. [41] are listed in Table 2.

Grid-1 Grid-2 Grid-3

-1.0E+05 -1.2E+05 -1.4E+05 -1.6E+05 -1.8E+05 -2.0E+05

3.4. Grid independence tests

-2.2E+05 -2.4E+05 -2.6E+05 -2.8E+05 -3.0E+05

89

1

2

3

4

5

6

Distance along Z-axis (m) Fig. 4. Total heat flux profile at line (x = 0, y = 3) along Z-axis.

3.3. Reaction kinetics model CFD modeling in combustion application using the global mechanisms can be found in the literature [41,6,42]. The simplest oxidation mechanism assumes that products of the chemical reactions consist only of CO2 and H2O and is used in case of air combustion. The physical situation that this assumption reasonably approximates is a diffusion flame suspended in the flow field at relatively high temperature. Here, the oxygen diffuses across the boundary layer to meet methane in a small well-defined reaction zone. The high temperature of the flame accelerates the local homogeneous kinetics, and mostly produces CO2 and H2O. The replacement of inert N2 with a chemically reactive compound, CO2, in case of oxyfuel combustion influences the importance of some of the elementary reactions governing the combustion and requires a modification of the global multistep reaction mechanisms to make them valid under oxy-fuel conditions [43]. The modified two-step hydrocarbon oxidation mechanism by Andersen et al. [41] is used in the

It is a very important issue in the numerical solution to ensure that the obtained results are grid independent. For this purpose, three different discretized geometries were examined in this study. They are listed in Table 3. It is found that the deviation of the results with increasing the level of discretization above 1,335,180 cells did not exceed 0.01%. The temperature profiles along Z-axis for the three grids were plotted in Fig. 3. The maximum variation in temperature between Grid-1 and Grid-3 is calculated to be 1.6% however; it is reduced to 0.2% in case of Grid-3 as compared to Grid-2. Furthermore, total heat flux has been checked in the analysis. The profiles of the total heat flux along Z-axis at front wall and y = 3 m are plotted in Fig. 4. The difference between Grid-3 and Grid-1 is found to be 0.9%. The deviation of 0.4% is computed for Grid-2 related to Grid-3. It should be mentioned from the above discussion that the variation in the results if Grid-3 is used in the solution will be insignificant. 4. Results and discussions 4.1. Models validation Validation of the computational models applied in this study is obtained through comparisons with the measurement of Andersson experimental work for air–fuel and oxy-fuel combustion [22,44]. The experiment was conducted on the100 kW oxy-fuel combustion test unit that connected to the Chalmers 12 MW research boiler. The combustor is down-fired with a cylindrical

Fig. 5. Combustion chamber of the Chalmers 100 kW oxy-fuel unit with details of the burner [26].

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2000 EXP EWBM SGG(0.2 1/m) SGG(0.4 1/m) WSGG[Smith(1982)]

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1800 1700 1600 1500 1400 1300 1200 1100 1000 900

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Radial distance from center line (m) Fig. 9. CO2 concentration at distance 0.384 m from the burner, OF21 combustion. Fig. 6. Temperature profile at distance 0.384 m from the burner with different radiation models, air combustion.

2000 0.2

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0.175 0.15 0.125 0.1 0.075

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Fig. 7. CO2 concentration at distance 1.4 m from the burner, air combustion.

2

3

4

5

6

7

Distance along Z-axis (m)

0.4

Radial distance from center line (m)

Fig. 10. Temperature profile at line (x = 3.264, y = 1.0675) along Z-axis, air combustion.

1700

1450 EXP EWBM SGG(0.2 1/m) SGG(0.4 1/m) WSGG[Andersson(3+1)] WSGG[Andersson(4+1)] WSGG[Smith(1982)] SGG(0.31 1/m)

1350 1300

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Radial distance from center line (m) Fig. 8. Temperature profile at distance 0.553 m from the burner with different radiation models, OF21 combustion.

refractory lined reactor which measures 0.8 m in inner diameter and 2.4 m in inner height. Fig. 5 illustrates the schematic of the

Fig. 11. Temperature profile at line (x = 3.264, y = 1.0675) along Z-axis, OF21 combustion.

combustion test unit with details of the burner. Three test conditions were considered in their work. The parameters of these three cases are: (1) Air-firing (O2 @ 21% Vol and N2 @79% Vol), (2) OF21

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1800 EWBM Leckner Perry SGG(0.1 1/m) SGG(0.18 1/m) SGG(0.25 1/m) WSGG4

Temperature (K)

1700 1600 1500 1400 1300 1200

0

1

2

3

4

5

6

Distance along Z-axis (m) Fig. 12. Temperature profile at line (x = 4.539, y = 4) along Z-axis, OF27 combustion.

Fig. 13. Temperature profiles at line (x = 3.264, y = 1.0675) along Z-axis for different combustion cases, EWBM.

Fig. 14. Specific thermal capacity profiles at line (x = 3.264, y = 1.0675) along Zaxis for different combustion cases, EWBM.

(O2 @ 21% Vol and CO2 @79% Vol) and (3) OF27 (O2 @ 27% Vol and CO2 @73% Vol). All tests were performed for propane gas fuel (C3H8) burnet at an excess air factor of 1.15 (15% excessive air). The feed gas temperature is between 25 and 30 °C. Heat input is

Fig. 15. Contours for temperature of vertical plane passing through the middle burners 2 and 5 (x = 4.539 m), EWBM.

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Fig. 17. Contours for CH4 mass fraction of vertical plane passing through the middle burners 2 and 5 (x = 4.539 m), EWBM.

Fig. 16. Contours for temperature of horizontal plane passing through the upper burners (y = 0 m), EWBM.

adjusted to be 80 kW h. The fuel mass flow rate through the fuel lance is 1.74 g/s. flows having volume rates of 37 m3/h and 54 m3/h are fed through primary and secondary air lances, respectively. The total heat absorption is 48.7 kW in the air case and

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Fig. 18. Turbulent viscosity profiles at line (x = 3.264, y = 1.0675) along Z-axis for different combustion cases, EWBM.

45.8 kW for the OF21 case. Fig. 6 illustrates radial temperature distribution at distance 0.384 m from the burner. It is found that the temperatures are over-estimated by all models. The maximum discrepancy is about 20%. The effective absorption coefficient of 0.4 (1/m) predicts higher temperature by 17% compared to the measurements whereas the absorption coefficient of 0.2 (1/m). Those differences in the results between experimental and numerical model using the SGG radiation model may be attributed to the calculations of the absorption coefficient as shown in the figure. Basically, an optimal value of SGG model effective absorption coefficient for a given situation can be found by trial and error by comparing the numerical results obtained using the SGG model with experimental data. Thus, the SGG radiation model absorption coefficient can be optimized using the experimental data. The comparison in Fig. 6 supports this concept. The experimental data are in good agreement with the EWBM except in the region near the center of the furnace. The difference between the EWBM and the WSGG model is less than 1%. In addition, CO2 concentrations are considered in the validation, they are under-predicted in numerical solution. However, the difference is about 3% as shown in Fig. 7. In general, temperature, velocity and species concentration can be predicted using CFD models with error of about 20% in the air–fuel combustion case. In case of OF21 combustion, Fig. 8 shows the temperature profile at distance 0.553 m from the burner. It is found that the temperature predicted by the EWBM is above the measured values by 3.8%. In addition, three grey one clear gas WSGG model, which is introduced by Andersson and Johansson [22], leads to temperature results with error of 4%. The absorption coefficient of 0.2 (1/m) over-predicts the temperature by 7.5%. The more accurate results are obtained if the absorption coefficient of 0.4 (1/m) is used in the solution, the difference will not exceed +4%. As discussed in description part for the basic assumptions for the SGG radiation model, the optimal value of the absorption coefficient for any one situation is not generally optimal for another. That’s why there are fewer differences in comparison with the experimental data in Fig. 3 as compared to those large differences in Fig. 6. The WSGG model over-predicts the temperature by 5.5%. It is noted in Fig. 9 that the computed CO2 concentrations are in good agreement with experimental data and the error less than 5%. In addition, a comparison between experimental and numerical results was made using the same radiation model, EWBM, in our previous work (see Ref. [36]). In this work [36], an atmospheric diffusion oxy-combustion flame in a gas turbine model combustor has been investigated experimentally and numerically.

Fig. 19. Contours for CO2 mass fraction of vertical plane passing through the middle burners 2 and 5 (x = 4.539 m), EWBM.

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Oxy-combustion and emission characterization, flame stabilization and oxy-combustion model validation analyses were the main goals of this research work. The combustor was fuelled with CH4 and a mixture of CO2 and O2 as oxidizer. The same modified twostep oxy-combustion reaction kinetics model for methane-oxygen combustion has been used like the present study and the same radiation model, EWBM, was applied in order to predict accurately the oxy-combustion characteristics. Both experimental and numerical results were in a very good agreement. 4.2. Performance of gas radiation models It was found, in the air–fuel combustion as shown in Fig. 10, that the weighted sum of grey gas model (WSGG) introduced by Smith et al. [45] predicts higher temperatures by 0.39% compared to the EWBM. The SGG model with absorption coefficient equal to 0.25 (1/m) under-predicts the temperature by 4.5% while the absorption coefficient of 0.18 (1/m) leads to lower results by 3.3%. The deviation in the temperature is reduced to 0.37% in case of the absorption coefficient has a value of 0.1 (1/m). In the case of OF21 combustion, Fig. 11 represents the temperature profiles at line located between first and second columns of burners in the mid-way between the rows of burners along Z-axis (i.e. x = 3.264 m, y = 1.0675 m), the results of four grey one WSGG model developed by Andersson and Johansson et al. [22] are in good agreement with those obtained in case of the EWBM. It over-predicts the temperature by 1.2%. Leckner model results in increased temperature values by about 7.9% whereas Perry model over-estimates the temperature by 2.8%. Simple grey gas model with absorption coefficient of 0.18 (1/m) exhibits more accurate results with difference of less than 0.89%. The results of simple grey gas model with the absorption coefficient equal to 0.25 (1/m) are under-predicted by 2.1%. In addition, temperature distributions at x = 4.539 m and y = 4 m along Z-axis are shown in Fig. 12. In the same trend, Leckner model, Perry model, and WSGG model over-predict the temperature by 15%, 5% and 1.2% respectively. Simple grey gas model leads to error of 2.8% when absorption coefficient of 0.25 (1/m) is used. This error is reduced to 1.35% in case the absorption coefficient equal to 0.18 (1/m). It should be emphasized that the maximum difference in the result when the absorption coefficient is selected from the range of 0.25 (1/ m) to 0.1 (1/m) will not exceed 4.3%. 4.3. Characteristics of oxy-fuel and air–fuel combustion processes The effects of replacing N2 by CO2 as in the oxy-fuel combustion are discussed for this boiler in this section. It is clear from the temperature profiles in Fig. 13 that the temperatures are lower in the case of oxy-fuel combustion compared to air–fuel combustion; reduction reaches up to 21% for OF21 and 18% for OF27. It is thought that the reason of this reduction is attributed to the higher thermal capacity of CO2 compared to N2. Fig. 14 demonstrates the specific thermal capacity profiles at line (x = 3.264, y = 1.0675) along Z-axis for the air–fuel combustion and the oxy-fuel combustion cases, it indicates higher specific thermal capacity in the case of the oxy-fuel combustion in comparison to that of air–fuel combustion. This explains the lower temperature levels in oxy-fuel combustion. Increasing the CO2 recirculation percentage results in higher specific thermal capacity in the combustion products and, thus, resulting in lower temperature levels. In addition to this reason, the radiative emissivity and absorptivity of the CO2 is higher when it is compared to N2 which is transparent to the radiation energy and because of this, flame cooling effects exhibited in the oxy-fuel combustion cases. Figs. 15 and 16 show a comparison between the temperature contours of the air–fuel case and the two oxy-fuel combustion

Fig. 20. Contours of radiation heat flux for air–fuel and oxyfuel combustion at the front, top and left walls of the furnace, EWBM.

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cases. The contours are taken in a vertical plane passing through the middle burners (x = 4.539 m) and horizontal plane passing through the upper burners (y = 0 m). It is clear from the figures that the temperature levels in the oxy-fuel combustion cases are lower in comparison to the air–fuel combustion case. As explained above, the specific heat capacity in the oxy-fuel combustion is higher than that of air–fuel combustion. However, as CO2 mass percentage increases, the temperature levels are reduced, as indicated by Figs. 15b and 16b. It is noted that the combustion rate is slower in the case of oxy-fuel combustion as compared to that of air-fired combustion, and this leading to extending the burning zone causing the flame length to increase. It is also shown that the temperature rise is slower in the oxy-fuel combustion cases in comparison to air–fuel combustion and this is attributed to the higher specific heat of CO2. In Fig. 16 and for burner number 3, left burner, the flame is extended due to the effects of the exit flow. The left burner is the closest burner to the exit section of the boiler and that’s why the flame is extended and the combustion is delayed. In the same figure and for the right burner, burner number 2, it’s far away from the exit section and the flow velocity around this burner is small. This may justify the short and wide flame for the right burner. The fuel burning rate is also affected by replacing N2 by CO2. Fig. 17 shows the contours of CH4 concentration in the air–fuel combustion and oxy-fuel combustion. It is noted that the fuel consumption rate is slower in the oxy-fuel combustion cases. Fig. 17b indicates further reduction in fuel burning rate as the CO2 percentage is increased. In order to clarify the influence of oxy-fuel combustion on the burning rate, the turbulent viscosity for the cases of air–fuel and oxy-fuel combustion were computed and are presented. Fig. 18 shows the turbulent viscosity profiles at line (x = 3.264, y = 1.0675) along Z-axis for the three combustion cases. It is noted that the higher turbulent viscosity and hence higher mixing rates in the case of the oxy-fuel combustion in comparison to those of air–fuel combustion accelerates the reduction in flame temperature and therefore decreases the fuel consumption rate (i.e. CO2 acts as a cooling gas). This explains the lower levels of temperature in the oxy-fuel combustion. In our previous work [36], an oxycombustion gas turbine combustor flame has been characterized in details through the measurement of by measuring the exhaust gas temperatures and species concentrations and comparing them with those from the numerical model. In this work, it is found that the combustion stability is improved with increasing the percentage of O2 at inlet however there is a limitation in temperature (see Ref. [35] for more details). Fig. 19 shows the contours of the CO2 concentrations of vertical plane passing through the middle burners 2 and 5 (x = 4.539 m). The CO2 concentrations rise from around 14% in the case of air–fuel combustion to above 80% in the oxy-fuel combustion in most of the furnace volume. Figs. 20 and 21 show the contours of total heat flux (radiative + convective) and radiation heat flux for air–fuel and oxy-fuel combustion at the front, top and left walls of the furnace. The negative sign of the heat flux means the flux from the walls to the adjacent gases. It is found that the radiation heat flux represents more than 80% of the total heat flux in the furnace in case of air–fuel combustion and about 70% in oxy-fuel combustion and this is justifying the importance of selecting the appropriate gas radiation models in order to quantify its value. Finally, it is found that the total heat flux on the walls in case of air–fuel combustion is higher than that of oxy-fuel combustion (OF21 and OF27) and this is due to the higher temperature in the air–fuel combustion. Total heat flux profiles on the front wall (x = 0) and y = 1.0675 along Z-axis for air–fuel and oxy-fuel combustion are plotted in Fig. 22.

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Fig. 21. Contours of total heat flux for air–fuel and oxyfuel combustion at the front, top and left walls of the furnace, EWBM.

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Fig. 22. Total heat flux profiles at line (x = 0, y = 1.0675) along Z-axis for different combustion cases, EWBM.

5. Conclusion Different gas radiation models were used in CFD modeling of the typical industrial water tube boiler and their influence on the results was investigated. It is found that Leckner model and Perry model over-predict the temperature compared to the exponential wide band model. Weighted-sum-of-grey-gases model can predict accurate results compared to the benchmark model, however, it requires new parameters for different ratios of H2O and CO2. It is a computationally efficient option for CFD simulation where there is a need for a simple and accurate gas radiation model. One of the limitations of Weighted-sum-of-grey-gases model and Perry model is that they are not applicable for pressures other than one atmosphere. The exponential wide band model and Leckner model are valid for use for various pressure and ratios of CO2 and H2O. The influence of these models on the prediction of gases concentrations is very limited. An optimal value of the absorption coefficient can be determined by comparing the results to the more accurate model (i.e. EWBM). The influence of the CO2 circulation on the oxy-fuel combustion characteristics was investigated. It is found that the temperature levels are reduced in the case of oxyfuel in comparison to the air–fuel combustion case. It is also found that higher specific thermal capacity in the combustion products are obtained as the CO2 recirculation is increased. Thus, lower temperature levels are exhibited in the case of oxy-fuel combustion. The fuel consumption rates are slower in the oxy-fuel combustion case in comparison to the air–fuel combustion case. It is also shown that the energy absorbed is much higher in the case of the air–fuel combustion along the surfaces. Acknowledgements The authors wish to acknowledge the support received from King Abdulaziz City for Science and Technology (KACST) through The Vice-Rectorship of Applied and Scientific Research at KFUPM under KACST project# AT-29-89.

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