Two-phase Turbulence Models in Eulerian-Eulerian ...

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ScienceDirect Procedia Engineering 102 (2015) 1677 – 1696

The 7th World Congress on Particle Technology (WCPT7)

Two-Phase Turbulence Models in Eulerian-Eulerian Simulation of Gas-Particle Flows and Coal Combustion Lixing Zhou* Department of Engineering Mechanics, Tsinghua University Beijing, China

Abstract Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gasLagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen’s “particle-trackingfluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-H-kp”, “unified second-order moment (USM)” and “non-linear k-H-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-4” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them. © Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2014The TheAuthors. Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS)

* Corresponding author. Tel.: 86-10-62782231; fax: 86-10-62781824. E-mail address: [email protected]

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS)

doi:10.1016/j.proeng.2015.01.304

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Key Words: Gas-particle flows; Coal combustion; Eulerian-Eulerian simulation; Turbulence model

1. Introduction It is well known that for simulation of dispersed multiphase flows (gas-particle/droplet flows; bubble-liquid flows) there are two approaches to treat the dispersed phase: trajectory or Lagrangian approach (including DEM, discrete element method) and pseudo-fluid approach. Hence we have Eulerian-Lagrangian (E-L) and EulerianEulerian (E-E) simulation. The latter is frequently called two-fluid modeling. Many engineering applications, including the commercial computer codes, adopt E-L models, but E-E models have their specific features. It was pointed by Crowe [1] that “the advantage of the two-fluid model is that the algorithm developed for the conveying phase can be easily modified for the particulate phase. Also the storage and computational time are not as excessive as it may be for the trajectory models”. The key problem of two-fluid modeling is the closure models of particle turbulence (particle turbulent fluctuation), leading to particle diffusion/dispersion. Earlier closure models for the particle turbulence are based on the idea of Hinze-Tchen’s particle-tracking-fluid theory of particle fluctuation, originally proposed by Tchen, and finally developed by Hinze [2]. According to Hinze-Tchen’s model, particle fluctuation should be always weaker than the fluid fluctuation and the larger the particle size, the weaker the particle fluctuation. Hence larger particles should diffuse slower than smaller particles. However, in the experiments of enclosed gas-particle jets done by Zhou et al.[3]it was found that 165Pm particles diffuse faster than 26Pm particles. Therefore, a transport equation theory of particle turbulence was proposed by Zhou and Huang [4], and a k-H-kp two-phase turbulence model against the kH-Ap model was proposed and used to simulate a gas-particle jet. Subsequently, for anisotropic gas-particle flows, a unified second-order moment (USM) or two-phase Reynolds stress equation model was proposed [5, 6]. Furthermore, to simplify the USM model, a non-linear k-H-kp model was proposed, it can still keep the features of anisotropic two-phase turbulence, but can save much more time than the USM model. Most of two-fluid models cannot well account for the particle-wall interactions. A particle-wall collision model accounting for wall roughness was developed by us. For simulating dense gas-particle flows existing two-fluid modeling is based on the kinetic theory of particles, which cannot account for the particle turbulence. Although some investigators attempt to combine the k-H-kp model with the kinetic theory (k-H-kp-4 model and k-H-kp-Hp-4 model), but these models cannot simulate anisotropic two-phase turbulence and the two-phase velocity correlation is not correctly closed. Hence, a USM-4 was proposed, in order to account for both large-scale particle fluctuations due to turbulence and small-scale particle fluctuations due to inter-particle collision. Besides, the turbulence modulation by the particle wake effect was studied by large-eddy simulation, and the anisotropic sub-grid scale two-phase stress models for two-fluid large-eddy simulation were also studied. For simulating gas-particle two-phase combustion, including pulverized-coal/spray combustion, most of investigators adopt Eulerian-Lagrangian approach. The advantage of E-L simulation is that it can give detailed history of particle temperature and mass change, but it needs large computation time, if a large number of particles is taken into account. Unlike the widely used Eulerian gas-Lagrangian particle models, two versions of two-fluid models were proposed by us, that is, a full two-fluid (FTF) model and a two-fluid-trajectory model (continuum gas and continuum-trajectory model or CT model of particle phase) for simulating reacting gas-particle flows and coal combustion. Both of them are based on Eulerian gas-phase equations, Eulerian particle continuity and momentum equations. The CT model uses Lagrangian equations to predict the particle temperature and mass change along the streamlines given by the Eulerian predictions. The FTF model uses three sets of particle continuity equations-particle number density, particle daf-coal ( dry and ash-free coal ) mass and particle moisture mass equations, to account for the coal-particle history effect due to moisture evaporation, coal devolatilization and char combustion, and also the Eulerian particle temperature equation. In the following paragraphs a brief review of these studies will be given.

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2 The USM and k-HH-kp Two-Phase Turbulence Models The particle turbulent fluctuation in dilute gas-particle flows is a dominant factor leading to particle dispersion. In the framework of two-fluid models, Tchen first considered the single-particle fluctuating motion in a fluid eddy, and afterwards Hinze [2] used the Taylor’s statistical theory of turbulence to obtain the Hinze-Tchen’s model for the ratio of the particle viscosity over the gas viscosity as (2-1) Q p /Q f (k p / k f ) 2 (1  W r1 /W T ) 1

U s d 2p /(18P ), W T

where W r1

k /H

Q is the kinematic viscosity, D is the diffusion coefficient, k is the turbulent kinetic energy, Wr1 is the Stokes’ particle relaxation time, WT is the gas turbulence time scale, Us is particle material density, P is gas dynamic viscosity and H is the dissipation rate of gas turbulent kinetic energy. The subscripts p and f denote particle and fluid respectively. This model can simply be denoted as an “Ap model”(algebraic particle turbulence model). It is used together with the gas turbulence k-H model, constituting a k-H-Ap two-phase turbulence model, and even nowadays is widely adopted as particle dispersion models in two-fluid models in many commercial codes. As above indicated, according to Eq.(1), the particle fluctuation should be always smaller than the gas fluctuation and the larger the particle size, the smaller the particle fluctuation. However, in contrast to what predicted by the Ap model, the LDV and PDPA measurements show that the particle turbulence intensity is larger than the gas one in the whole flow field of confined gas-particle jets and in the reverse flow zones of recirculating and swirling gas-particle flows, and the particle turbulence intensity increases with the increase of the particle size in a certain size range. Based on the concept of particle turbulence transport, starting from two-phase instantaneous momentum equations, using Reynolds expansion and time averaging, an energy equation model (kp model) of particle turbulence was derived and closed [4] and subsequently a two-phase Reynolds stress transport equation model, i.e. a time-averaged unified second-order moment (USM) two-phase turbulence model was proposed [5,6]. The gas and particle Reynolds stress equations in their closed form are obtained as w w (Uv i v j )  (UVk v i v j ) Dij  Pij  G p  3 ij  Hij ij wt wx k w w ( N p v pi v pj )  ( N p Vpk v pi v pj ) D p,ij  Pp,ij  H p,ij wt wx k

(2-2) (2-3)

where v denotes velocity, U denotes density, N denotes number density, D ij, Pij , 3 ij, H ij are terms having the same meanings and are closed using the same methods as those well known in single-phase fluid Reynolds stress equations. The new source term for two-phase flows Up G p,ij ¦ ( v pi v j  v pjv i  2 v i v j ) W p rp is a phase interaction term expressing the fluid Reynolds stress production/destruction due to fluid-particle interaction. The transport equation of dissipation rate of fluid turbulent kinetic energy for two-phase flows is:

w w (UH)  (UVk H) wt wx k

w wH k H (c H v k v l )  [cH1(G  G p )  cH2UH] wx H wx l k

(2-4)

where the new source term is

Gp

Up

¦W p

rp

( v pi v i  v i v i ) .

For a closed system, beside Eqs. (2), (3) and (4), the transport equations of n p v pi , also should be used. For example, the transport equations of

n p v pj , n pn p , v pi v j , v pjv i

v pi v j and particle turbulent kinetic energy are derived

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based on the fluid and particle momentum equations and closed as:

w w ( v pi v j )  ( Vk  Vpk ) ( v pi v j ) wt wx k 

w w [( Qe  Q p ) ( v pi v j )] wx k wx k

wVpi wVj 1 H [U v pi v pj  U v i v j  (U  U p ) v pi v j ]  ( v pk v j )  v pi v i Gij  v k v pi k UWrp wx k wx k (2-5)

w w ( N pk p )  ( N p Vpk k p ) wt wx k

kp wk p w ( N pcsp v pk v pl )  Pp  N pHp wx k Hp wx l

˄2-6˅

where the last term on the right-hand side of Eq.(5) is closed by assuming that the dissipation of two-phase velocity correlation is proportional to the dissipation rate of the fluid turbulent kinetic energy. and

Hp



1 1 [ v pi v i  v pi v pi  ( Vi  Vpi )n p v pi ] Wrp Np

Equations (2-1)-(2-6) constitute the unified second-order moment two-phase turbulence model. It is found that the k-H-kp model is a reduced form of the USM model in case of nearly isotropic turbulent flows, which consists of the following expressions and equations

wVpi wVpj wV wVj 2 2  kGij  Q t ( i  ) ; v pi v pj k pGij  Qp ( ) wx j wx i 3 wx j wx i 3 Q p wN p Qp wN p ˈ n p v pj  n p v pi  Vp wx j Vp wx i viv j

w w (Uk)  (UVjk) wt wx j

w Pe wk ( )  G  G p  UH wx j Vk wx j

w w (UH)  (UVjH) wt wx j

w Pe wH H ( )  [cH1(G  G p )  cH2UH] wx j VH wx j k

w( N p k p ) wt



 

w ( N p k p v pk ) wx k

w N p Q p wk p ( )  Pp  N p H p wx k V p wx k



2 k 2p · wk pg · w §§ k ¨ ¨¨ cs  c kp ¸¸ ¸ wx k ©¨ © H H p ¹ wx k ¹¸



w w k pg  Vk  Vpk k pg wt wx k 

wv pi wv · 1 1§ 1  v pi v k i ¸¸  k pg U p k p  Uk  (U  U p )k pg  ¨¨ v i v pk 2© wx k ¹ We wx k UWrp





(2-7)

(2-8)

(2-9)

(2-10) (2-11)

(2-12)

Figure 2-1 shows the simulation results of particle number density in wind-sand flows behind an obstacle, reported by Laslandes and Sacre [7], using both k-H-kp and k-H-Ap models and their comparison with experiments. It is seen that the k-H-kp model is much better than the k-H-Ap model in predicting the particle dispersion.

Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

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Fig.2-1 Particle Number Density

(a) Bubble (b) Liquid Fig.2-2 The Normal Reynolds Stress in Vertical Direction For simulating complex turbulent bubble-liquid-solid flows, a second-order moment three-phase turbulence model is proposed [8]. The derivation procedure is similar to that used for single-phase flows. This model was used to simulate bubble-liquid flows in a bubble column measured at the Ohio State University. Figure 2-2 gives simulated bubble and liquid normal Reynolds stress in vertical direction. It is seen that in the case studied the prediction results are in very good agreement with the PIV measurement results, and the bubble turbulence is much stronger than the liquid turbulence. In other words, bubbles induce liquid turbulence. 3. The Non-Linear k-HH-kp Model It has been found that the conventional or linear k-H-kp model is rather simple and can well simulate nonswirling and weakly swirling gas-particle flows. However, for strongly swirling flows the USM model should be better, but the USM model is rather complex and is not convenient for engineering application. A best compromise between the reasonability and simplicity is either an implicit algebraic two-phase Reynolds stress model, or a nonlinear k-H-kp two-phase turbulence model, i.e. an explicit algebraic two-phase Reynolds stress model. Since the algebraic Reynolds stress models frequently cause some divergence problem due to lack of diffusion terms in the momentum equation, particularly in 3-D flows. A non-linear k-H-kp two-phase turbulence model is developed by Zhou and Gu [9]. This is because the momentum equations and k, H, kp equations have the same form for both linear and nonlinear k-H-kp models, so it is easier to obtain the convergent results.

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When using the full second-order moment model for a three-dimensional flows, we should solve 26 differential equations, including 6 gas Reynolds stress equations, 6 particle Reynolds stress equations, 9 two-phase velocity correlation equations, 1 dissipation-rate equation for gas turbulent kinetic energy, 3 particle diffusion mass-flux equations and 1 equation for the mean square value of particle number density fluctuation. In order to reduce the computation time and simultaneously to retain the anisotropic features of the turbulence model, as that done in single-phase turbulence models, an algebraic two-phase stress model is obtained by simplifying the stress transport equations [9]. Neglecting the convection and diffusion terns in the two-phase Reynolds stress and two-phase velocity correlation equations of the USM model, the algebraic expressions of twophase Reynolds stresses and two-phase velocity correlation can be obtained as:

wVj k wVi k 2 ( v pi v j  v i v pj  2v i v j ) )  v jv k (1  O ) kGij  O ( v i v k wx k c1UH H wx k 3 W rp § wV wV · 1 ¨ v pi v pk pj  v pjv pk pi ¸  ( v i v pj  v pi v j ) v pi v pj  ¨ 2 © wx k wx k ¸¹ 2 U UWrp § wV wV · Up UWrp 1 ¨ v pi v k j  v jv pk pi ¸  v pi v pj  v pi v i Gij v pi v j  viv j  ¨ ¸ U  Up U  Up We U  Up © wx k wx k ¹ U  U p viv j

(3-1) (3-2) (3-3)

To construct a non-linear k-H-kp two-phase turbulence model, we can transform Eqs. (3-1), (3-2), and (3-3) into the following explicit form, on the right-hand side of which there are no terms containing

v pi v j , v pi v pj , v i v j .

The obtained nonlinear stress-strain-rate relationships written to quadratic-power terms of the strain rates are:

§ § wV wV · wV · G1G ij  G2 ¨ wVi  j ¸  G3 ¨ pi  pj ¸ ¨ wx j wxi ¸ ¨ wx j wxi ¸¹ © ¹ © § wV § wV j wV · wV j § wV wV · · § wV § wV wV · · wV · wV § wV ¨ i  k ¸ ¸  G5 ¨ pi ¨ pj  pk ¸  pj ¨¨ pi  pk ¸¸ ¸  G4 ¨ i ¨  k ¸ ¸ ¨ wxk ¨ wxk ¨ wxk ¨ wxk wx j ¸ wxk ¨© wxk wxi ¸¹ ¸ wxi ¹ ¸ wx j ¹ wxk © wxk © © ¹ © ¹ © ¹ § · § wV § wV pj wV pk · wV j § wV pi wV pk · · wV pi § wV j wVk · wV pj § wVi wVk · ¸ ¨ ¸ ¸ ¸ ¨ ¨¨ ¸¸ ¸  G7 ¨     G6 ¨ i ¨  ¸ ¨ wxk wx j ¸ wxk ¨© wxk wxi ¸¹ ¸ ¨ wxk ¨ wxk ¸ ¨ w w w x x x x w x w j k k i k © ¹ © ¹ © ¹ © ¹ © ¹ § § wVi wV pi ·§ wV j wV pj · · (3-4) ¸¸¨¨ ¸¸   G8 ¨¨ ¨¨  wxk ¸¹ ¸¹ © © wxk wxk ¹© wxk

vi v j

§ § wV wV · wV · P1G ij  P2 ¨ wVi  j ¸  P3 ¨ pi  pj ¸ ¨ wx j wxi ¸ ¨ wx j wxi ¸¹ © ¹ © § wV § wV j wV · wV j § wV wV · · § wV § wV wV · · wV · wV § wV ¨¨ i  k ¸¸ ¸  P5 ¨ pi ¨ pj  pk ¸  pj ¨¨ pi  pk ¸¸ ¸  P4 ¨ i ¨  k ¸ ¨ wxk ¨ wxk ¨ wxk ¨ wxk wx j ¸ wxk © wxk wxi ¹ ¸ wxi ¹ ¸ wx j ¸¹ wxk © wxk © © ¹ © ¹ © ¹ § wV pi § wV j wV · wV pj § wV wV · · § wV § wV pj wV pk · wV j § wV pi wV pk · · ¨ ¸ ¨¨ i  k ¸¸ ¸ ¸¸ ¸  P7 ¨ ¨¨  k ¸   P6 ¨ i ¨  ¸ ¨ ¸ ¨ wxk ¨ wxk ¸ ¨ x x x x w w w x x x x w w w w w wxi ¹ ¸ j ¹ k © k i ¹¹ j ¹ k © wxk © © © k © k ¹ § § wVi wV pi ·§ wV j wV pj · · (3-5) ¸¸¨¨ ¸¸ ¸  P8 ¨¨ ¨¨   ¸ w w w w x x x x k k k k © ¹ © ¹ © ¹

v pi v pj

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§ wV wV j · § wV § wV wV · wV · ¸  T3 ¨ pi  pj ¸  T4 ¨ j  pi ¸ T1Gij  T2 ¨ i  ¨ wx j ¨ wxi ¨ wx j wxi ¸ wxi ¸¹ wx j ¸¹ © © © ¹ wV j § wVi wVk · wVpi § wVpj wVpk · wVpj § wVpi wVpk · wV § wV j wVk ·¸ ¨ ¸  T8 ¸ ¨ ¨¨ ¸¸  T7  T6  T5 i ¨     ¨ ¸ ¨ ¸ wxk © wxk wx j ¹ wxk © wxk wxi ¹ wx k © wx k wx j ¹ wx k ¨© wx k wx i ¸¹ wV pi § wV j wVk · wV § · ¨ ¸  T10 pj §¨ wVi  wVk ·¸  T11 wVi ¨ wV pj  wV pk ¸  T12 wV j §¨ wV pi  wV pk ·¸  T9  ¸ ¨ wxk ¨© wxk wx j ¸¹ wxk © wxk wxi ¹ wxk ¨© wxk wx j ¸¹ wxk ¨© wxk wxi ¸¹ wV · · § wV § wV pj wV j · wV pj § wVi wV pi · · § wV § wV wV · wV § wV ¸¸  ¨¨ ¸¸ ¸  T14 ¨ j ¨¨ pi  i ¸¸  pi ¨¨ j  pj ¸¸ ¸  T13 ¨¨ i ¨¨   ¸ ¨ wx w w w w w w w w w x x x x x x x x x x w wxk ¹ ¸¹ k ¹ k © k k ¹¹ k¹ k © k © k© k © k© k (3-6) where all of the coefficients G1aG8, P1aP8, T1aT14 are functions of k, H , k p , k pg , U p , U , and W rp . v pi v j

The variables k,

H , kp

and

k pg are determined by the following governing equations

w Pe wk w w ( Uk )  ( UV j k ) ( )  U vi vk wvi  UH  U p 2k pg  2k wx j V k wx j wx j wt W rp wxk w UH  w UVk H w wt wxk wxk







w w U pk p  U pV pk k p wt wxk

(3-7)

· § · wH · H § § k U ¨¨ UcH vk vl ¸¸  ¨ cH 1¨  U vi vk wvi  p 2k pg  2k ¸  cH 2 UH ¸ ¸ ¸ wxl ¹ k ¨ ¨© H wxk W rp © ¹ © ¹



w wxk

§ ¨ U p ckp ¨ ©

kp

Hp

v pk v pl

(3-8)

wk p · ¸  U v v wv pi  U p 2k  2k p pi pk pg p wxl ¸¹ wxk W rp (3-9)

 





w w k pg  Vk  V pk k pg wt wxk

w wxk

§§ k · wk pg · kp ¨¨c v v  c ¸  1 U k  Uk  ( U  U )k v pk v pl ¸ p p p pg s k l kp ¸ ¨¨ H ¸ Hp ¹ wxl ¹ UW rp ©©

wv pi 1§ wv · 1  v pi vk i ¸¸  k pg  ¨¨ vi v pk 2© wxk wxk ¹ W e





(3-10)

The nonlinear k-H-kp (NKP) model was used to simulate swirling gas-particle flows with a swirl number of 0.47, measured by Sommerfeld and Qiu [10] using PDPA and compared with the USM model. Figures 3-1 and 3-2 show the NKP and USM predicted particle tangential time-averaged and RMS fluctuation velocities respectively and their comparison with the experimental results. It is seen that in most regions of the flow field, the difference between two model predictions is small and both of them are in good agreement with experiments. In general, the NKP model can predict what the USM model can predict, but the former can save almost 50% computational time for a 2D flow with small geometrical sizes. It is expected that for 3-D flows with large geometrical sizes, the NKP model can save much more computational time. Keeping in mind that in engineering application the accuracy of predicting the two-phase averaged velocities is more important, one can consider that the NKP model can be used instead of the USM model

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1.0

0

2

4

6 0

2

4

6 0

2

0

2

0

2

4

r/R 0.5

0.0

0.5

1.0

52

0 Exp

195

155 USM

NKP

315

X[mm]

Fig. 3-1 Tangential Velocity of 45Pm Particles (m/s, s=0.47) -1.0

0

2

4

0

2

0 4

1

2

0 3

1

0

1

r/R -0.5

0.0

0.5

1.0

0

52 Exp

155 NKP

195 USM

315

X[mm]

Fig.3-2 Tangential Fluctuation Velocity of 45Pm Particles (m/s, s=0.47) 4 Model for Dense Gas-Particle Flows 4. The USM-4 In dense gas-particle flows there are both large-scale particle fluctuations due to particle turbulence and smallscale particle fluctuations due to inter-particle collisions. A USM-4 two-phase turbulence model for dense gasparticle flows was proposed by Yu and Zhou et al.[11]. In this model the gas turbulence and particle large-scale fluctuation are predicted using the USM two-phase turbulence model, and the particle small-scale fluctuation due to inter-particle collisions is predicted using the particle pseudo-temperature equation--4 equation, given by Gidaspow’s kinetic theory [12]. This is not a simple superposition, since there are interaction terms in the particle Reynolds stress equations and the 4 equation. Some of the closed USM-4 model equations are: The gas Reynolds stress equation





w D g U gm u giu gj w D g U gmU gk u giu gj  wt wxk where

Gg , gp,ij



wt where

Gp , gp,ij

Dg ,ij  Pg ,ij  3 g ,ij  H g ,ij  Gg , gp,ij

(4-1)

E u piugj  ugiu pj  2ugiugj

The particle Reynolds stress equation

w D p U pm u piu pj



 wD

p

U pmU pk u piu pj wxk



Dp ,ij  Pp,ij  3 p,ij  H p,ij  Gp,gp,ij

E u piugj  u pjugi  2u piu pj

The equations of dissipation rate of turbulent kinetic energy for gas and particle phases:

(4-2)

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w D g U gmH g wt



Hg kg

>c P H1

where Gg , gp



w D p U pmH p wt 

Hp kp

 wD

g

g

U gmU gkH g

 Gg , gp  cH 2D g U gmH g

2E kgp  kg , cH 3

 wD p

w wxk

wxk

p

U pmU pkH p wxk

p , gp

§ wH g · k ¨ C g D g U gm g u gk u gl ¸ ¨ ¸ w x H g l ¹ ©

@

(4-3)

1.8

>C P  G  C Hp ,1



Hp , 2

§ wH · k ¨ D p U pmC pd p u pku pl p ¸ ¨ wxl ¸¹ Hp ©

w wxk

D p U pmH p

@

(4-4)

2E k pg  k p

where E is the inverse relaxation time, Gp, gp The two-phase velocity correlation equation:

wu piu gj wt

 U gk  U pk

wu piu gj wxk

Dg , p,ij  Pg , p,ij  3 g , p,ij  H g , p,ij  Tg , p,ij

(4-5)

The particle pseudo-temperature transport equation:







~ 4º w D p U pmU pku 3 ª w D p U pm4 pk  « » wt wxk 2 ¬« ¼»



w wxk

§3 w4 ¨¨ D p U pm u pk T  *4 wxk ©2

· ¸¸ ¹

2

wU pl § § wU pk wU pi · wU pi 2 ·§ wU pl ·¸ ¸¸  P p ¨¨   P pH p  Pp  ¨ [ p  P p ¸¨¨ J wxk ¹ wxk wxl 3 © ¹© wxl ¸¹ © wxi

(4-6)

where the notations in Eq.(4-6) are the same as that given by Gidaspow [12]. The interaction between the large-scale and small-scale particle fluctuations is the third term on the right-hand-side of Eq.(4-6), expressing the effect of the dissipation rate of particle turbulent kinetic energy on the particle pseudo-temperature. Simulation results for dense gas-particle flows in a downer measured by Wang, Bai and Jin [13] indicate that for predicting the particle volume fraction (Fig.4-1) and particle velocity (Fig.4-2) the USM-4 model is much better than the DSM-4 model, not accounting for particle turbulence, the USM model, not accounting for inter-particle collision and the k-H-kp-4 model, not accounting for the anisotropy of turbulence. Figure 4-3 shows the predicted particle horizontal RMS fluctuation velocity for horizontal gas-particle pipe flows measured By Kussin and Sommerfeld [14]. It is seen that the USM-4 model can more reasonably predict particle RMS fluctuation velocities than other models.

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Experiment USM4 k-HkP4

Particle volume fraction

0.035

0.030

DSM-4 USM

0.025

0.020

0.015

0.010

0.005 0.0

0.2

r/R

0.4

0.6

0.8

1.0

Fig.4-1 Particle Volume Fraction 8

Experiment USM4 k-HkP4 DSM-4 USM

Particle Velocity(m/s)

7 6 5 4 3 2 1 0.0

0.2

0.4

r/R

0.6

0.8

1.0

Fig.4-2 Particle Time-Averaged Velocity 1.0

Exp. USM-4 USM k-H -kP-4

0.8

y/H

0.6 0.4 0.2 0.0 0.00

0.05

0.10 ucpc uin

0.15

Fig.4-3 Particle Horizontal RMS Fluctuation Velocity

0.20

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

5. Two-Phase Turbulence Modeling accounting for the Particle Wake Effect on Turbulence Modulation It is well known that the wake formation and shedding of vortices behind particles will induce gas turbulence. Some investigators proposed semi-empirical turbulence enhancement models, however these models either have not been used to predict practical gas-particle flows, or give only qualitative results. Most numerical predictions of separated flows passing over a sphere are obtained by RANS modeling. There is an increasing interest in the use of LES to predict flows past a particle; however, no statistical data of turbulence enhancement are given. To solve this problem, the gas turbulent flows passing over a single particle is simulated using LES [15], and the prediction results of turbulence enhancement are compared with the experimental data and RANS modeling results, in order to validate a turbulence enhancement model by the particle wake effect. The proposed turbulence enhancement model is then incorporated into a second-order moment two-phase turbulence model to simulate practical gas-particle flows. The prediction results by the two-phase turbulence models taking and not taking into account the particle wake effect are compared with each other and with the experimental data. The gas flows passing over a single particle at Rep>400 are simulated using LES and RANS modeling. The filtered continuity and momentum equations are

wU w UU k 0  wt wxk

(5-1)

w wxk

w UU i  w UU iU k wxk wt

§ wU i ¨¨ P © wxk

· wp wW ik ¸¸   ¹ wxi wxk

(5-2)

The Smagorinsky-Lilly model is adopted for the sub-grid scale stress Wik. The numerical procedure and boundary conditions are similar to those given in the last paragraph. For RANS modeling the baseline version of the gas Reynolds stress equation model is taken. Figures 5-1 and 5-2 give the predicted vorticity map by LES and velocity vectors by RANS respectively. The vortex structures in the wake behind the particle can be seen clearly.

 Fig.5-2 Velocity vectors by RANS

Fig.5-1 Vorticity map by LES 4

2.6

5

2.4

-2

'K / m . s

-2

2.0

3

1

1.8

2

2

2

calculation fit line

2.2

calculation fit line

'K / m . s

ux / Uin

4

exp. LES RANS

3

2

1.6 1.4 1.2

1

1.0 0

0 0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

x/m

Fig.5-3 The RMS fluctuation velocity behind the particle

5

6

7

8

9

10

Urel / m . s

11

12

13

14

-1

Fig.5-4 Turbulence enhancement for various inlet velocitiesdp = 1000 μm)

0.8 0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

dp / m

Fig.5-5 Turbulence enhancement for various particle sizes (Urel = 10 m/s)

The predicted gas RMS fluctuation velocity by LES and RANS modeling are close to the experimental results, and the LES results are better than the RANS results (Fig. 5-3). Figures 5-4 and 5-5 show the relationship of the

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

turbulence enhancement due to particle wake effect. In Fig.5-4, when the particle size keeps constant, as dp=1000μm, the magnitude of the turbulence enhancement due to the wake effect increases with the increase of inlet velocity, it 2 , where 'K is the difference between the maximal turbulent obeys approximately a 2nd-power law, 'K v U rel kinetic energy behind the particle and the inlet turbulent kinetic energy. In Fig.5-5, when the inlet velocity keeps constant, as Urel=10m/s, the magnitude of the turbulence enhancement increases with the increase of particle size, it obeys approximately a linear law, 'K v d p . The increase of turbulence intensity by the particle wake effect for different inlet velocities and particle sizes can be summarized as 2 'K v U rel ˜dp Accounting for the effect of both particle size and inlet velocity, the source term of turbulence enhancement by particles for two-phase flows should be 2 G p, w v U rel d p For practical gas-particle flows with multiple particles, the production source term should be directly proportional to the number density n p or the particle volume fraction D p , where D p n pS d 3p / 6 , so we have

2

G p , w v n pU rel d p v

D pU rel 2 dp

2

The conventional particle source term (production/dissipation term) due to the existence of point-source particles in the gas turbulent kinetic energy equation or Reynolds stress equation is

Gp

D pUp (2v pi vi  2k f ) W rp

Performing dimension analysis, the following turbulence enhancement source term by the particle wake effect is proposed as 2 U pD pU rel G pw c

W rp

where the empirical constant c is taken as c=3.0. W rp

U p d p2 18P f (1  Re

2/3 p

/ 6)

Re p

D f U f d p U f U p Pf

The turbulence enhancement model is incorporated into the second -order moment two-phase turbulence model for simulating practical gas-particle flows. The gas Reynolds stress equation becomes



w D f U f u fi u fj wt

 wD U U g

f

fk

u fi u fj

wxk



D f ,ij  Pf ,ij 3 f ,ij  H f ,ij  G fp,ij  G pwG ij (5-3)

 The transport equation of the dissipation rate of gas turbulent kinetic energy becomes



wDf UfH f wt

Hf kf

 wD

f

U f U fk H f wxk



w wxk

§ k wH · ¨ C f D f U f f u fk u fl f ¸  1 >CH 1 Pf  G f , fp  CH 2D f U f H f @   ¨ Hf wxl ¸¹ W e ©

CH 3G pw 

5-4) The proposed model was used to simulate vertical gas-particle flows, measured in [16]. Figures 5-6 to 5-8 give the RMS gas fluctuation velocities for different sizes of particles. It is found that the results obtained using the model accounting for the particle wake effect are in much better agreement with the experimental results than those obtained using the model not accounting for the particle wake effect in predicting the following phenomena: 0.2 mm

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

particles attenuate gas turbulence only, 0.5 mm particles enhance or attenuate gas turbulence at different locations, and 1mm particles enhance gas turbulence intensity only. 0.20

experiment m=0, U=13.4m/s experiment m=0.5, U=13.1m/s m=0, U=13.4m/s m=0.5, U=13.1m/s (wake effect) m=0.5, U=13.1m/s (no wake effect)

0.10

0.05

0.00 -1.0

experiment m=0, U=13.4m/s experiment m=3.4, U=10.7m/s m=0, U=13.4m/s m=3.4, U=10.7m/s (wake effect) m=3.4, U=10.7m/s (no wake effect)

0.15

u/ U

u/ U

0.15

0.20

0.10

0.05

-0.5

0.0

0.5

0.00 -1.0

1.0

-0.5

0.0

r/R

0.5

1.0

r/R

Fig.5-6 Air turbulence intensity of 0.2 mm particles

Fig.5-7 Air turbulence intensity of 0.5 mm particles

0.20

experiment m=0, U=13.4m/s experiment m=0.6,U=13.4m/s m=0, U=13.4m/s m=0.6,U=13.4m/s (wake effect) m=0.6,U=13.4m/s (no wake effect)

u/ U

0.15

0.10

0.05

0.00 -1.0

-0.5

0.0

0.5

1.0

r/R

Fig.5-8 Air turbulence intensity of 1 mm particles 6. A Particle-Wall Collision Model Accounting for the Wall Roughness It is well known that the particle-wall collisions are directly treated in the Lagrangian discrete particle simulation. In the early-developed Eulerian-Eulerian or two-fluid modeling of fluid-particle flows, the particle-wall collision was not taken into account, and zero normal particle velocity and zero normal gradient of other particle variables at the wall are assumed as wI V pw 0 ( wyp ) w 0 This model is equivalent to the full reflection condition without energy loss in the Lagrangian approach, which is obviously not true in practical gas-particle flows where particle-wall collision plays important role. A particle-wall collision model in the framework of two-fluid approach, taking the restitution, friction and wall roughness into account was proposed by the present author [17]. For example, the particle number density, longitudinal velocity and longitudinal component of normal Reynolds stresses at the walls are given as

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

1 1 1 V p1 ) N p1 (1  )(1  2 e 3 2k p / 3

N pb

(6-1)

1 V pb (V p1  V p1 f )(1  Dc2 ) 3 u pu p

(6-2)

1 u p1u p1{3  Dc2 [2  f 2 (1  e)]} 3 1 2  v p1vp1(1  e)[3 f 2  Dc2 (1  2 f 2 )]  u p1v p1 f [3  Dc2 ( 2e  3)] 3 3 1 1 2 2 2 2  U p1U p1Dc f (1  e)  V p1V p1[3ef  Dc2 (1  e  2ef 2 )]  U p1V p1Dc2 f (1  2e) 3 3 3

b

(6-3) where f, e and D denote the friction coefficient, restitution coefficient and wall roughness respectively, the capital alphabets U and V denote time-averaged particle velocities and lower-case alphabets u and v denote particle fluctuation velocities, the subscript b denotes the values at the wall, and the subscript 1 denotes the values in the near-wall grid nodes. These equations imply that the particle number density, velocity components and Reynolds stresses will change under the effect of particle-wall collision due to friction, restitution and wall roughness, and not obey the law of zero normal velocity and zero-gradient of other variables. The wall roughness can lead to redistribution of particle Reynolds stress components after particle-wall collision. The predicted particle tangential time-averaged velocity (Fig.6-1) and RMS tangential fluctuation velocity (Fig.6-2) of swirling gas-particle flows measured by Sommerfeld and Qiu [10] show that the prediction results using the boundary condition “bc 2”, based on Eqs.(6-1) to (6-3), give lower near-wall particle tangential time-averaged and RMS fluctuation velocities due to the effect particle-wall collisions, in agreement with those observed in experiments, whereas the prediction results using the boundary condition “bc 1” , not accounting for the particle-wall collisions, give higher near-wall particle time-averaged and RMS fluctuation velocities, not in agreement with experimental results. 1.0

0.8

r/R

0.6

0.4

0.2

0.0

0

2

4 0

2

4 0

2

4 0

w p (m/s)

w p (m/s)

w p (m/s)

x=3mm

x=25mm

x=52mm

2

4 0

w p (m/s)

2 w p (m/s)

4

2 w p (m/s)

4

2 w p (m/s)

4

2 w p (m/s)

x=85mm x=112mm x=155mm x=195mm x=315mm Exp. bc1 bc2

Fig. 6-1 Particle tangential time-averaged velocity (m/s)

4

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696 1.0

0.8

r/R

0.6

0.4

0.2

0.0

0

1

0

1

w cpc (m/s)

w cpc (m/s)

x=3mm

x=25mm

0

1

2

w cpc (m/s)

x=52mm

1

w cpc (m/s)

2

1

w cpc (m/s)

2

1

w cpc (m/s)

2

0.5

w cpc (m/s)

1.0

0.5

w cpc (m/s)

1.0

x=85mm x=112mm x=155mm x=195mm x=315mm Exp. bc1 bc2

Fig. 6-2 Particle RMS tangential fluctuation velocity 7. Two-Fluid LES of Gas-Particle Flows In the framework of two-fluid or Eulerian-Eulerian LES, some investigators adopt the Smagorinsky SGS eddy viscosity model for both gas and particle phases without theoretical justification, and the interaction between two phases and the anisotropy of the two-phase SGS stresses are not taken into account. Extending the idea of the twophase turbulence models in RANS modeling, a unified second-order moment (USM) two-phase SGS model is proposed by the present author and his colleagues for two-fluid LES of gas-particle flows [18]. The proposed model is expected to fully account for the interaction between the gas and particle SGS stresses and their anisotropy. The LES-USM is used to simulate swirling gas-particle flows. For a two-fluid LES, neglecting the gravitational force, the filtered continuity and momentum equations for gas and particle phases can be obtained as:

w α kρk  w (α kρk u ki ) wt wx j

0 ˄k=g,p˅

˄7-1˅

w pg wτ g,ij wτ gs,ij α gρg w w α gρg u gi  (α gρg u gi u gj )    u pi  u gi wt wx j wx j wx j wx j τr











w w α pρp u pi  (α pρp u pi u pj ) wt wx j

wτ p,ij wx j



wτ ps,ij wx j

where the filtered gas and particle viscous forces are: wu gj wu gi wu gj 2 τ g,ij μ gl澠  )  μ gl G ij ; τ p,ij wx j wx i 3 wx j



μ p(

α gρ g τr



ugi  u pi

(7-2)

˄7-3˅

wu pi wu pj wu pj  ) 2 Pp G wx j wxi 3 wx j ij

The gas and particle subgrid scale (SGS) stresses are defined as:

τ gs,ij

ρg R gs,ij

-U g ( u gi u gj - u gi u gj ) ; τ ps,ij

ρp R ps.ij -U p ( u pi u pj - u pi u pj )

The SGS stresses of gas and particle phases can be given by the following transport equations:

w w sgs sgs sgs sgs (D g U g Rgs,ij )  (D g U g u gk Rgs,ij ) Dsgs g  Pg  G pg  Π g  ε g (7-4) wt wx k w w sgs sgs (D p U p R ps,ij )  (D p U p u pk Rps,ij ) Dsgs ˄7-5˅ p  Pp  ε p wt wx k

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

Other equations, like the SGS two-phase velocity correlation and SGS enery dissipation equations can be found in Ref. [18] . Figures 7-1 and 7-2 give the predicted two-phase tangential time-averaged and RMS fluctuation velocities respectively. It is seen that the LES-USM gives better results than those obtained by the RANS-USM. 1.0 1.0

0.8

0.8

0.6

r/R (/)

0.6

0.4

0.4

0.2

0.2

0.0

0.0 0

5

10

0

4

X=3mm

80

2

X=52mm Exp.

4

0

2

X=155mm LES

4

0

X=195mm

2

0

4

2

0

X=3mm

X=315mm

5

0

X=52mm

2

0

X=155mm

Exp.

RANS-USM

LES

2

0

X=195mm

2

4

X=315mm

RANS-USM

˄a˅gas (b˅particle Fig.7-1 Two-phase tangential time-averaged velocities 1.0 1.0

0.8 0.8

0.6

r/R ((/)

r/R (/)

0.6

0.4

0.4

0.2 0.2

0.0 0.0

0 0

3

X=3mm

0

2

X=52mm Exp.

0

2

0

X=155mm LES

2

X=195mm

RANS-USM

0

1

2

0

1

0

1

0

1

-1

0

1

2

2

X=315mm

X=3mm

X=52mm Exp.

X=155mm LES

X=195mm

X=315mm

RANS-USM

˄a˅gas (b) particle Fig.7-2 Two-phase tangential RMS fluctuation velocities

Fig.7-3 Instantaneous gas streamlines for two-phase swirling flows

Fig.7-4 Instantaneous particle streamlines for two-phase swirling flows The instantaneous gas and particle streamlines are shown in Figs.7-3 and 7-4. There are more complicated multiple recirculation zones of the gas flows (Fig.7-3), including a corner recirculation zone and many recirculation zones in the near axis and intermediate regions, than those of the time-averaged gas flows, where only a corner recirculation zone and a central recirculation zone are observed. The particle flow field (Fig.7-4) is different from the gas flow field. Particles at first concentrate in the near-axis zone and enter the near-corner recirculation zone, then gradually move to the wall under the effect of centrifugal force and turbulent diffusion, and finally concentrate in a thin layer adjacent to the wall. There are almost no recirculating flows of particles in the near-axis and downstream regions due to different inertia of two phases.

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8. Two-Fluid Modeling of Coal Combustion A full two-fluid model of coal combustion was proposed by the author [19]. The gas-phase continuity, momentum, energy and species equations are:



wU w  p =S  Uv j = -¦ n pm wt wx j p



(8-1)

> 





m wv w Uv i  w Uv jv i = - wp + wwx [P( wx j  wwxv i )] + Ugi  ¦ p n p v pi - v i  ncp vcpi j i j wt wx j wx i W p r



@ (8-2)



w U v cjv ic + v iS wx j

(8-3) § · w Uh + w Uv jh = w ¨¨ O wT ¸¸ - q r + ¦ n pQp - ¦ n pm ph p + WsQs - w Uvcjhc wt wx j wx j © wx j ¹ wx j p p







§ · w UYs + w Uv jYS = w ¨¨ DU wYS ¸¸ - WS - DS ¦ n pm p - w UYscvcj wt wx j wx j © wx j ¹ wx j p











˄8-4˅

The particle-phase equations are: Particle number density equation

wn p wt

+



w npv pj = - w ncpvcpj wx j wx j



˄8-5˅

Particle momentum equation

>

@

 w n p v pi + w n p v pjv pi = n pgi + 1 n p v i  v ki - nc p v pic  n pmp v i - v pi wt wx j Wr mp



w n p v pjc vc pi + v pj nc p vc pi + v pi nc p vc pj wx j



(8-6)

For the particle phase, beside the number density equations, there are three other continuity equations







+

w n pmp w w p + n p m p v pj = -mp ncp vcpj + n p m wt wx j wx j w n p mc



wt

w n pmw wt









(8-7)









(8-8)

w w c n pmc v pj = -mc ncp vcpj + n pm wx j wx j

+









w w w n p m w v pj = -mw ncp vcpj + n p m wx j wx j

Particle energy equation

(8-9)

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

















p np n pm w w n ph p + n p v pjh p = Q h - Q p - Q rp  h - hp wt wx j mp mp



w n p v pjh p + v pj n p h p + h p n p v pj wx j

(8-10)



For two-phase turbulence modeling, a k-H-kp model is used. For volatile and CO combustion in the comprehensive modeling of coal combustion, originally the conventional EBU-Arrhenius model is used. For radiative heat transfer a six-flux model is used. The NO formed in coal combustion consists of mainly thermal NO and fuel NO. For the reaction kinetics of thermal NO formation, the well-known Zeldovich mechanism is used. For the reaction kinetics of fuel NO formation, the DeSoete mechanism is used The special feature is the algebraic second-order moment (ASOM) turbulence-chemistry model for NO formation in turbulent combusting flows. The time-averaged reaction rate is

B U 2 [(Y1Y2  Y1/Y2/ ) K  Y1 K /Y2/  Y2 K /Y1/ ]

WS

where K

K

³

˄8-11˅

exp( E / RT )

exp( E / RT)p(T)dT , p(T) is the PDF of temperature. Assuming a top-hat PDF gives

K {exp[E / R (T  g1T/ 2 )]  exp[ E / R (T  g1T/ 2 )]} ; g T

T c2

______ ______ ______ ' ' ' ' ' ' The correlations K Y1 , K Y2 , Y1 Y2 in Eq.(51) can be determined by the following algebraic expressions ______ ' ' 1 2

YY

__

___

k 3 w Y w Y ______ C1 2 1 2 ; K 'Y1' H wx j wx j

___

___

___

k 3 w K w Y1 ______ ' ' ; Y2 K C1 2 H wx j wx j

___

k 3 w Y2 w K C1 2 H wx j wx j

(8-12)

where k , H are the turbulent kinetic energy and its dissipation rate. Simulation of coal combustion and NO formation [19] was carried out in a swirl combustor measured by Abbas et al. [20]. Figures 8-1 and 8-2 show the predicted and measured gas velocity and turbulent kinetic energy for isothermal flows respectively. 80

x=0.115m 80

x=0.205m 80

80

80

70

70

70

70

70

70

70

60

60

60

60

60

60

60

50

50

50

50

50

50

50

40

40

40

40

30

30

30

30

20

20

20

20

10

10

10

80

70

60

50

x=0.205m

x=0.375m

x=0.63m

40

40

40

40

30

30

30

30

20

20

20

20

10

10

10

10

0

0 -5

0

5

10

0 0

3

6

r(mm)

r(mm)

x=0.115m 80

0

0 -5

0

5

-5

0

x(m)

Fig. 8-1 Gas Axial Velocity (Pred  Exp)

5

0 -5

0

5

10

x=0.375m

2

4

6

x=0.63m

10

0 0

80

0 0

5

-4

0

4

8

x(m)

Fig 8-2. Turbulent Kinetic Energy (Pred  Exp)

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

x/d3=1.18 x/d4=2.74

x/d4=5.60

0.30

0.30

0.30

0.30

0.25

0.25

0.25

0.25

0.20

r(m)

x/d4=4.09

0.20

0.15

0.20

0.15

0.10

0.15

0.10

0.05

2000

800

1600

x/d3=4.09

0.30

0.30

0.30

0.25

0.25

0.25

0.25

0.20

0.20

0.20

0.20

0.15

0.15

0.15

0.15

0.10

0.10

0.10

0.10

0.05

0.05

0.05

0.05

0.00 600 1200

0.00 500 1000

x/d3=5.60

0.10

0.05

0.00 1000

x/d3=2.74

0.30

0.15

0.10

0.05

0.00

0.20

r(m)

x/d4=1.18

0.05

0.00 800

0.00 -600

0.00 1600

800

0

0

0.00 0

500

500

1600

NO(ppm)

t(K)

Fig.8-3 Temperature ( Pred. ƒ Exp.)

Fig. 8-4 NO Concentration ( Pred. ƒ Exp.)

1000 1.0

600

0.9

Burnout

NO(ppm)

800

400

0.8

200

0 0.4

0.6

0.8

1.0

1.2

1.4

swirl number

Fig.8-5 Averaged NO Concentration

0.7 0.4

0.6

0.8

1.0

1.2

1.4

Swirl Number

Fig.8-6 Coal Burn-Out Rate

Figure 8-3 gives the predicted and measured temperature profiles. Good agreement between predictions and experiments are obtained. Figure 8-4 shows the predicted NO concentration profiles and their comparison with the experimental results. The agreement is also good. Figures 8-5 and 8-6 give the predicted averaged NO concentration at the exit and burnout rate vs. as the swirl number respectively and their comparison with experimental results. Both predictions and experiments show the common tendency: as the swirl number increases the NO concentration at first will decrease and then will increase, whereas the burnout rate at first will increase and then will decrease. There is a quantitative discrepancy between predictions and experiments. The predicted lowest NO emission and highest burnout rate occur at the swirl number of 0.8, but the measured ones occur at the swirl number of 1.0. This discrepancy may be caused by numerical errors and inaccuracies of the models. The overall NO formation in coal combustion should be determined by the temperature, coal concentration and turbulent fluctuation. With the increase of swirl number from 0.5 to 0.8, the temperature increases not so much, but the coal concentration in the inlet zone increases and the turbulent fluctuation decreases. Therefore, the NO formation decreases. Conclusions (1) For two-fluid modeling of gas-particle and bubble-liquid flows the USM and k-H-kp two-phase turbulence models can more reasonably predict the particle/bubble turbulence than the traditional k-H-Ap model. (2) In dense gas-particle flows both particle large-scale fluctuation due to anisotropic particle turbulence and particle small-scale fluctuation due to inter-particle collision are important to particle dispersion. (3) The full two-fluid model of coal combustion together with an algebraic SOM turbulence-chemistry model can well simulate NO formation during coal combustion Acknowledgement This study was sponsored by the National Key Project of Fundamental Research of China under the Grant G19990222-07-08 many years ago and presently by the Key Project of National Natural Science Foundation of China under the Grant 51390493 and the Project under the Grant 51266008

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Lixing Zhou / Procedia Engineering 102 (2015) 1677 – 1696

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