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Ar-CO-liquid steel flow with decarburization chemical reaction in single snorkel refining furnace
International Journal of Heat and Mass Transfer 146 (2020) 118857
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Ar-CO-liquid steel flow with decarburization chemical reaction in single snorkel refining furnace Shifu Chen a,b, Hong Lei a,b,⇑, Meng Wang a,b, Bin Yang a,b, Weixue Dou b,c, Lishan Chang c, Hongwei Zhang a,b a
Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, 110004 Shenyang, China School of Metallurgy, Northeastern University, 110004 Shenyang, China c Jingye Iron and Steel Limited Company, Shijiazhuang 050400, China b
a r t i c l e
i n f o
Article history: Received 23 April 2019 Received in revised form 16 September 2019 Accepted 7 October 2019
Keywords: Single snorkel refining furnace Single snorkel RH Vacuum Ar-CO-liquid steel flow Continuous-flow decarburization reaction Two-way coupling mathematical model
a b s t r a c t As a new style refining equipment developed from the traditional RH furnace, Single Snorkel Refining Furnace (SSRF), which is also called as single snorkel RH, is widely used for producing ultra-low carbon steel. However, the effect of CO gas on fluid flow and decarburization is not reported in the existing literatures. Based on the Eulerian-Eulerian approach, a two-way coupling mathematical model considering CO gas is proposed to investigate the coupling phenomenon of Ar-CO-liquid steel flow and decarburization in SSRF. And the industrial experimental data is employed to validate the numerical result. In comparison with the one-way coupling model, the numerical result predicted by the two-way coupling model is closer to the industrial experimental data. The CO mole number, which is generated by the overall decarburization process, is about 3 times the argon mole number blown into the ladle, and the CO generation rate is greater than argon blowing rate at the first 12 min. Because of the stirring effect of CO gas, there are the more complex fluid flow, the stronger mass transfer, the greater decarburization rate and the lower carbon mass concentration in the liquid steel during decarburization. Besides, the Ar plume area predicted by the two-way coupling model is larger and it is closer to the center line of the snorkel. Therefore, the effect of CO gas on the fluid flow cannot be ignored and the two-way coupling model can describe the metallurgical phenomena in SSRF more precisely. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction During the secondary refining process, RH (Rheinstahl-Heraeus) furnace, which plays a quite vital role in producing high quality steel, is widely applied to remove carbon, oxygen, nitrogen, hydrogen and inclusions in liquid steel. In order to improve the refining effect and promote the productivity, many researchers have proposed many measures in traditional RH furnace, such as increasing the height of the vacuum chamber, changing the diameter and number of the snorkel, introducing multi-function nozzles [1,2]. Single Snorkel Refining Furnace (SSRF), which is also called Single Snorkel RH, is developed by China steel company in the 1970s [3,4]. In SSRF, the up and down snorkels in traditional RH are combined into a large cylindrical snorkel, as shown in Fig. 1, and the argon gas is blown into the liquid steel from the bottom of the ladle. Up to now, many researchers paid attention to the gas liquid flow pattern [1,5–9,13], circulation flow rate [10–13], mixing ⇑ Corresponding author at: Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, 110004 Shenyang, China. E-mail address: [email protected] (H. Lei). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118857 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
phenomenon [13–16], gas volume fraction distribution [13,17,18] and decarburization mechanism [19–25] of traditional RH. But in comparison with traditional RH, only a few of papers focused on the fluid flow and decarburization of SSRF. In order to improve the degassing captivity of DH (Dortmund-Hörder) refining process, Nippon Steel Corporation in Japan transformed DH into REDA (Revolutionary Degassing Activator) to produce ultra-low carbon steel in 1990s [26]. For the fluid flow system, Yang et al. [3] simulated the three-dimensional flow field of liquid steel to optimize the configuration and operation parameters of an 80 t SSRF, and Dai et al. [27] investigated the mixing efficiency and the circulation rate by different injection positions and snorkel diameters in SSRF. By the water model, Rui et al. [28] studied the effect of elliptical snorkel on the decarburization rate in SSRF. You et al. [4] developed a dynamic model, which considered three decarburization sites: argon bubble surface, inner site of the vacuum chamber and free surface of the vacuum chamber. With a one-way coupling mathematical model, Geng et al. [29] investigated the decarburization, the fluid flow and the inclusion collision-aggregation in SSRF. However, some important problems about the modelling of the metallurgical phenomenon in SSRF are far from being solved. During the SSRF decarburization process, a large amount of CO
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Nomenclature A d D ! g h k k/;Ar k/;L K !CO M M p Q r S t ! u
area (m2) diameter (m) diffusion coefficient (m2/s) gravitational acceleration (m/s2) distance (m) turbulent kinetic energy (m2/s2) mass transfer coefficient from liquid steel to bubble surface (m/s) mass transfer coefficient from liquid steel to reaction boundary (m/s) decarburization equilibrium constant momentum transfer (N/m3) molar mass (g/mol) pressure (Pa) circulation flow rate (t/min) radius (m) source term for carbon-oxygen reaction time (s) velocity (m/s)
V
volume (m3)
Greek symbols r interfacial energy (N/m) e turbulent eddy dissipation (m2/s3) a volume fraction b unit conversion coefficient of pressure q density (kg/m3) l viscosity (Pas) w mass concentration w equilibrium mass concentration Subscript / cir eff g l mix
C and O circulation effective gas liquid steel mixing
Fig. 1. Schematic of Single Snorkel Refining Furnace and two-way coupling calculation methodology.
bubbles are generated in the liquid steel. Like argon bubbles, CO bubbles also affect the multiphase flow field, and the related gasliquid system is in an unsteady state because the number of CO bubbles changes with the decarburization time, as shown in Fig. 1. In the meantime, the decarburization rate is also be influenced by the stirring effect of CO bubbles. But all the fluid flow and the decarburization models reported in the existing literatures are one-way coupling models, which do not take into account of the influence of CO bubbles. Based on the Eulerian-Eulerian approach, a two-way coupling mathematical model considering the stirring effect of CO bubbles is proposed to investigate the coupling phenomenon of unsteady argon-CO-liquid steel flow and decarburization in SSRF. Then, the industrial experimental data is applied to validate the mathematical model. Certainly, this paper also shows the effect of CO bubbles on the multiphase flow and the decarburization in detail.
2. Mathematical model Fig. 2 gives the solution methodology of the mathematical model in detail. The two-way coupling mathematical model is carried out to investigate the Ar-CO-liquid flow based on the decarburization chemical reaction in SSRF. Considering the generation of CO gas caused by the carbon and oxygen in the liquid steel, the Eulerian-Eulerian multiphase flow model, the standard k e turbulent model and the interphase momentum transfer model are employed to get the unsteady Ar-CO-liquid steel flow field. And the transport equations of carbon and oxygen and decarburization model are calculated to obtain the instantaneous spatial distribution of CO bubbles. It should be noted that, the behavior of CO bubbles generated by decarburization is an unsteady process, so the effect of CO bubbles on the fluid flow is also an unsteady process.
S. Chen et al. / International Journal of Heat and Mass Transfer 146 (2020) 118857
ll;t ¼ ql C l
k
3
2
ð2Þ
e
Based on the research model proposed by Sato et al. [33,34], the bubble-induced turbulence can be formulated by:
! lg;t ¼ C g;l ql ag dg ! u g u l
ð3Þ
where the model constant C g;l is 0.6. According to Jakobsen et al. [35], the effective viscosity of argon gas and CO gas are determined by the effective viscosity of liquid steel in the multiphase flow.
Fig. 2. Flow chart of the multiphase flow and decarburization by the two-way coupling mathematical model.
lAr;eff ¼
qAr l ql l;eff
ð4Þ
lCO;eff ¼
qCO l ql l;eff
ð5Þ
qAr and qCO are the constant density of argon gas and CO gas, respectively. In the multiphase momentum equations in Table 1, the inter! phase momentum transfer (M ) between the gas phase (argon and CO) and the liquid phase comes from the interfacial forces. As shown in Table 2, the interfacial forces can be divided into five categories: drag force, lift force, virtual mass force, wall lubrication force and turbulent dispersion force [30,36]. For the argon gas blown into SSRF, the initial diameter of argon bubble ðdAr Þ can be formulated by [18,30,31,41]:
Because of the complicated metallurgical phenomenon and the heavy numerical computational load, some assumptions are applied to simplify the mathematical model. (1) The fluid flow in SSRF is not affected by the top slag, there is not any chemical reactions between liquid steel and slag, and the free surfaces of the vacuum chamber and the ladle are flat [9,17,18,23,30,31]. (2) The gas-liquid flow and the decarburization occur at 1873 K in SSRF, and the fluid flow is a Newtonian incompressible viscous flow [9,17,23,30,31]. (3) The interactions (such as breakup and coalescence) among bubbles are neglected, and the bubbles are spheres [9,17,21,30,31]. (4) The chemical reaction between carbon and oxygen in the liquid steel takes place on the bubble surface, the free surface of the vacuum chamber and the inner site of the vacuum chamber [4,18,21,24,25,31]. (5) CO bubbles are generated at once after the chemical reaction between carbon and oxygen occurs, which have a same size as argon bubbles. (6) The argon blowing rate does not change during the SSRF refining process [23–25,27,29–31]. 2.1. Multiphase fluid flow In the current work, the flow fields about argon gas, CO gas and liquid steel are calculated by the multiphase fluid model (EulerianEulerian approach). The related governing equations are summarized in Table 1. The effective viscosity of liquid steel (ll;eff ) consists of three items [33,34]: the molecular viscosity (ll ), the turbulent viscosity (ll;t ) and the bubble-induced turbulence (lg;t ).
ll;eff ¼ ll þ ll;t þ lg;t With:
ð1Þ
dAr ¼ 0:091
rAr ql
0:5 u0:44 Ar;0
ð6Þ
where rAr is the interfacial energy between argon gas and liquid steel, N/m; uAr;0 is the argon blowing velocity determined by the circulation argon flow rate, m/s. According to the research of Tatsuoka et al. [42], under high vacuum environment, the main position for bubbles expansion is near the free surface of vacuum chamber. Therefore, the bubble size is treated as a constant. 2.2. Decarburization process In the SSRF, the decarburization chemical reaction can be expressed as:
½C þ ½O ¼ COðgÞ
ð7Þ
For the decarburization process, the decarburization rate is controlled by the mass transfer of carbon and oxygen in liquid steel [21,25]. And the mass conservation can be formulated by [25]:
@ ! ðq w/ Þ þ r ðql u l w/ Þ ¼ r ðql D/;eff rw/ Þ S/ @t l
ð7Þ
where / denotes C and O; D/;eff is the effective diffusion coefficient, m2/s; S/ is the source term of carbon and oxygen transport equation in the three sites during decarburization. The decarburization rate of three sites is given in Table 3, and the carbon and oxygen mass concentration at equilibrium state are determined by the thermodynamic equation about decarburization chemical reaction. For the decarburization at the vacuum chamber free surface, based on the research of Takahashi et al. [21], the effective decarburization area is 10 times the cross section of the vacuum chamber because of the splash and fluctuation of liquid steel [18,22,31]. For the decarburization at the argon bubbles surface, the mass transfer coefficient k/;Ar can be formulated by [24,31]:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k/;Ar ¼ 2 D/ uslip Ar =pdAr
ð8Þ
where uslip Ar is the slip velocity, m/s; D/ is the diffusion coefficient,
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Table 1 Governing equations of fluid flow. Items
Equations
List of symbols
! @ @t ðqAr aAr Þ þ r qAr aAr u Ar ¼ 0 ! MCO dwC @ @t ðqCO aCO Þ þ r qCO aCO u CO ¼ ql MC dt ! @ @t ðql al Þ þ r ql al u l ¼ 0 ! ! ! @ @t qAr aAr u Ar þ r qAr aAr u Ar u Ar
! ! T ! ! ¼ aAr rp þ r aAr lAr;eff r u Ar þ r u Ar þ qAr aAr g þ M Ar;l ! ! ! @ @t qCO aCO u CO þ r qCO aCO u CO u CO
T ! ! ! ! ¼ aCO rp þ r aCO lCO;eff r u CO þ r u CO þ qCO aCO g þ M CO;l ! ! ! @ @t ql al u l þ r ql al u l u l
! T ! ! ! ! ¼ al rp þ r al ll;eff r u l þ r u l þ ql al g þM l;Ar þ M l;CO
Continuity equation
Momentum equation
! r u l kÞ i ðal ql ll;t ¼ r al ll þ rk r k þ al ðGk ql eÞ þ al ql k
Turbulent kinetic energy equation
@ðal ql kÞ @t hþ
Turbulent eddy dissipation equation
@ðal ql eÞ @t hþ
a is the volume fraction, aAr þ aCO þ al ¼ 1; q is the
! density, kg/m3; u is the velocity, m/s; t is the time, s; M is the molar mass, g/mol; wC is the mass concentration of dissolved carbon.
! g is the gravitational acceleration, m/s2; p is the ! pressure, Pa; leff is the effective viscosity, Pas; M Ar;l and ! M CO;l are the momentum transfer of gas (Ar and CO) !
phase relative to liquid steel, respectively, N/m3; Ml;Ar !
and M l;CO are the momentum transfer of liquid steel relative to gas (Ar and CO), respectively, N/m3.
k is the turbulent kinetic energy, m2/s2; e is the turbulent eddy dissipation, m2/s3; C l ¼ 0:09, C 1 ¼ 1:44, C 2 ¼ 1:92, rk ¼ 1:0, re ¼ 1:3 [13,16,32].
! r u l eÞ i ðal ql ll þ lrl;te r e þ al ke ðC 1 Gk C 2 ql eÞ þ al ql e
¼ r al
Table 2 Interfacial forces model. Items
Equations ! ! ! ! ! F D ¼ 34 CdDg ag ql u g u l u g u l ! ! ! ! F L ¼ C L ag ql u l u g r u l ! ! ! D u F VM ¼ C VM ag ql DlDtu l gDt g
Drag force [37] Lift force [37,38] Virtual Mass Force [18,38] Wall Lubrication Force [39]
! ! ! 2 ! F WL ¼ C WL ag ql u l u g n W
Turbulent Dispersion Force [40]
! mt;l rag ral F TD ¼ C TD C D SC;l ag al
2rCO rCO
C D is the drag force coefficient. C L is the lift force coefficient. C VM is the virtual mass coefficient. ! C WL is the wall lubrication force coefficient; n W is the unit normal vector away from the wall. C TD is the turbulent dispersion force coefficient; mt;l is the turbulent kinematic viscosity of the liquid phase.
DC ¼ 2:24 108 m2 =s and DO ¼ 1:26 108 m2 =s [24,31]. For the decarburization at the inner site of the vacuum chamber, the dissolved carbon and oxygen are at the supersaturated state, and the impact of CO nucleation pressure is considered in the mathematical model. The partial pressure of CO ðPCO Þ can be formulated by [4,18,43]:
PCO ¼ PV þ bql gh þ b
List of symbols
ð9Þ
where PV is the vacuum chamber pressure, Pa; rCO is the interfacial energy, N/m; b is the unit conversion coefficient of pressure.
2.3. Computational conditions Fig. 3 gives the geometric parameters and mesh configuration of SSRF. The computational domain is discretized into 250 000 grids by ICEM CFD. For the nozzle at the bottom of the ladle, the inlet velocity of argon gas is determined by the circulation argon flow rate, and the inlet velocity of CO gas equals zero. Degassing condition is applied at the free surfaces of the vacuum chamber and the ladle through which argon gas and CO gas can escape from the free surface at the terminal floating velocity, but liquid steel cannot. Besides, no slip wall condition is applied to all walls in SSRF. In the vacuum chamber, the pressure is 67 Pa. Physical properties
Table 3 Governing equations of decarburization. Items
Equations
Decarburization rate at the vacuum chamber free surface [18,21,22,31]
dw/1 dt
Decarburization rate at the argon bubbles surface [24,31]
dw/2 dt
Decarburization rate at the inner site of the vacuum chamber [21,31]
dw/3 dt
List of symbols
M/ 10AV h¼ 1000 V min kC;L 1000 MC wC
M/ 1000
i wC ; kO;L 1000 MO wO wO
6aAr AAr pd3Ar
¼ h i 1000 min kC;Ar 1000 MC wC wC ; kO;Ar MO wO wO ¼ k0 hh0 ðK CO wC wO P CO Þ
AV is the cross section area of vacuum chamber, m2; V is the volume of liquid steel, m3; w/ is the equilibrium mass concentration; k/;L is the mass transfer coefficient from liquid steel to reaction boundary, kC;L ¼ 6:0 104 m=s, kO;L ¼ 4:5 104 m=s [24]. k/;Ar is the mass transfer coefficient from liquid steel to bubble surface [24,31]; AAr is the surface area, m2; dAr is the diameter, m. k0 is a constant of 3 107 ð1=Pa sÞ at h0 ¼ 0:15 m [21]; h is the distance from CO bubble to liquid surface, m; K CO is the decarburization equilibrium constant; P CO is the spatial pressure of CO.
S. Chen et al. / International Journal of Heat and Mass Transfer 146 (2020) 118857
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four different grids. The maximum difference about Q cir is only 0.21% and the maximum difference about tmix is only 1.59%. Thus, the 250 000 grids is applied to finish the following calculation in order to reduce the computational load. To validate the mathematical model, two industrial experiments of SSRF decarburization are conducted in a steel company, as shown in Fig. 4. The monitor position of carbon mass concentration in the numerical simulation is consistent with the sampling position in the industrial experiment. During the industrial decarburization process, the liquid steel is sampled every 5 min with the Ultra-low Carbon Sampler, and the spectrum analytical method is used to measure the carbon content in liquid steel. Fig. 4 shows that the predicted carbon mass concentration agrees well with the industrial experimental data. The carbon mass concentration predicted by the two-way coupling model is less than that predicted by the one-way coupling model. For the experiment of wC0 ¼ 225 106 , the error between the one-way coupling model and the industrial experiment is 48.39% and 22.78% at the 5th and 10th minute of decarburization, respectively. But the error between the two-way coupling model and the industrial experiment is 13.71% and 5.06% at the 5th and 10th minute of decarburization, respectively. And for the experiment of
Fig. 3. Geometric parameters and mesh configuration.
Table 4 Physical properties and numerical parameters. Items
Values
Density of liquid steel Viscosity of liquid steel Density of argon gas Density of CO gas Interfacial energy between argon bubble and liquid steel Interfacial energy between CO bubble and liquid steel Circulation argon flow rate Vacuum chamber pressure Initial carbon mass concentration
7000 kg/m3 0.0062 Pas 1.783 kg/m3 1.250 kg/m3 1.5 N/m [24] 1.9 N/m [43] 330 NL/min 67 Pa 225 106
Initial oxygen mass concentration
1135 106
and numerical parameters during the calculation are shown in Table 4. 2.4. Computational procedure In the current work, the computational fluid dynamics software CFX combined with the CFX Expression Language (CEL) is employed to investigate the multiphase flow and decarburization in SSRF. Partial differential equations are solved by the finite volume method. The time scale is 0.01 s and the convergence criteria is that the root-mean-square normalized residual of all variables is less than 105 . By parallel computing on 16 CPU cores, it takes about two weeks to finish a two-way coupling model calculation. 3. Results and discussions 3.1. Model validation To ensure the numerical results quite compelling and persuasive, the verification of grid independence is carried out by a steady flow field calculation. Table 5 gives the circulation flow rate (Q cir ) and the mixing time (tmix ) of liquid steel on the base of
wC0 ¼ 407 106 , the error between the one-way coupling model and the industrial experiment is 5.26%, 28.67% and 15.88% at the 5th, 15th and 25th minute of decarburization, respectively. But the error between the two-way coupling model and the industrial experiment is 4.68%, 7.17% and 3.82%, respectively. Thus, the carbon mass concentration predicted by the two-way coupling model is closer to the industrial results. Furthermore, it can be seen from Fig. 4 that the difference of the predicted carbon mass concentration between the one-way coupling model and the two-way coupling model increases with the increase of the decarburization time. At the 5th minute of decarburization, the difference rises 13.87% to 12:20 106 in the experiment of wC0 ¼ 225 106 and rises 9.62% to 17:32 106 in the experiment of wC0 ¼ 407 106 . As the chemical reaction between carbon and oxygen proceeds further, the difference decreases gradually because fewer CO bubbles are generated in the later stage of decarburization process with the decrease of the carbon and oxygen concentration in liquid steel. Because the equilibrium constant of the chemical reaction between carbon and oxygen is determined by the temperature in liquid steel, the CO bubbles during decarburization can only improve the decarburization kinetic conditions and increase the decarburization rate in SSRF. Therefore, the final equilibrium carbon mass concentration predicted by the twoway coupling model is the same as that predicted by the oneway coupling model. The Ar-CO-liquid steel flow and decarburization in the experiment of wC0 ¼ 225 106 are investigated in detail in the following results and discussions. 3.2. Liquid steel flow field during decarburization Figs. 5 and 6 give the unsteady liquid steel flow fields predicted by the one-way coupling model and the two-way coupling model in SSRF at the 5th minute during decarburization. These flow fields have some similar features. (1) With the help of floating argon bubbles blown from the bottom of the ladle, there is a large recirculation zone in SSRF: ladle -> snorkel -> vacuum chamber -> snorkel -> ladle. (2) A small recirculation zone appears near the free surface of ladle because of the driving effect of argon bubbles. In SSRF gas-liquid system, the two-way coupling model can describe the effect of CO bubbles on liquid steel flow but the one-way coupling model don’t consider the existence of CO bubbles. Thus, Figs. 5 and 6 also give the differences about the fluid flow at the 5th minute. (1) On the side of ladle away from the argon
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Table 5 Verification of grid independence. Items
Q cir , t/min tmix , s
Grids 200 000
250 000
300 000
350 000
33.16 123.92
33.15 124.56
33.09 123.44
33.10 125.40
cross-sectional planes of Ar plume are defined in the snorkel, as shown in Fig. 8. Fig. 9 gives the ratio between the Ar plume area (with the volume fraction of argon greater than 1%) and the cross-sectional plane area. It can be seen from that the difference of Ar plume area between the one-way coupling model and the two-way coupling model increases gradually from the bottom to the upper part of the snorkel. And the maximum Ar plume area ratio predicted by the two-way coupling model is 33.87% of the cross-sectional plane in Fig. 9, which is 2.23 times that predicted by the one-way coupling model. Consequently, the flow behavior of argon bubbles is changed significantly when the CO gas is considered in the two-way coupling model. 3.4. CO distribution during decarburization
Fig. 4. Comparison of predicted carbon mass concentration with the industrial experimental data.
bubbles main stream, there is a recirculation zone near the free surface of the ladle predicted by the two-way coupling model. (2) Near the free surface of the ladle, the fluid velocity predicted by the two-way coupling model is greater than that predicted by the one-way coupling model. (3) In the vacuum chamber and the upper part of snorkel, there are 4 recirculation zones predicted by the two-way coupling model and 2 recirculation zones predicted by the one-way coupling model. (4) In the snorkel, the velocity of liquid steel near the center line predicted by the twoway coupling model is greater than that predicted by the oneway coupling model. These differences come from the fact that the spatial distribution of CO bubbles is different from that of argon bubbles, which will be discussed in Section 3.4. 3.3. Ar distribution during decarburization As the essential factor driving the flow of liquid steel, the upward argon stream in the snorkel plays a crucial role in the multiphase flow and decarburization in SSRF. Fig. 7 shows that Ar plume region expands gradually with the floatation of argon bubbles, and the simulated fluid flow pattern is similar to the water model experiment result [28]. But there are also different features of Ar plume region between the one-way coupling model and the two-way coupling model. (1) In comparison with Fig. 7(b), the Ar plume region predicted by the one-way coupling model is narrow relatively, but the Ar plume region predicted by the two-way coupling model is wider due to the more recirculation zones and stronger turbulent flow in the vacuum chamber and the snorkel. (2) On the base of the one-way coupling model, most of argon bubbles are close to the snorkel wall, and a few argon bubbles escape from the liquid steel from the free surface of the ladle. But on the base of the two-way coupling model, the Ar plume region is closer to the center line of the snorkel, and there are only a few argon bubbles closing to the snorkel wall. In order to give the difference about the spatial distribution of argon predicted by different coupling models more intuitively, four
Fig. 10 shows the significant difference between CO generation rate and argon blowing rate predicted by two-way coupling model in SSRF. As the chemical reaction between carbon and oxygen proceeds, the carbon mass concentration decreases and CO generation rate slows down gradually during decarburization process. The maximum CO generation rate is 270.10 mol/min at the 1st minute, which is 18.33 times the argon blowing rate (14.73 mol/min). After the 12th minute, the CO generation rate is less than argon blowing rate. And the CO generation rate is 3.08 mol/min at the 20th minute. There are two interesting phenomena in Fig. 10. (1) CO generation rate is greater than the argon blowing rate at the first 12 min. (2) The amount of CO mole number is 991.52 mol, which is 3.37 times the argon mole number blown from the bottom of the ladle. Thus, the multiphase flow should consider both CO gas and argon gas during SSRF decarburization. Fig. 11 gives the spatial distribution of CO bubbles in SSRF at the 5th minute of decarburization predicted by the two-way coupling model. Most of CO bubbles appear near the free surface of the ladle and in the vacuum chamber and the snorkel. And the spatial distribution of CO bubbles corresponds with the recirculation zones near the free surface of the ladle and in the vacuum chamber and the snorkel, as shown in Fig. 6(a) and (c). Several reasons lead to such interesting phenomena. (1) In the current mathematical model, CO bubbles are generated at once after the chemical reaction between carbon and oxygen occurs. (2) As one important decarburization site, many CO bubbles are generated in the inner sites of the vacuum chamber, some CO bubbles escape from the free surface of the vacuum chamber directly, and other CO bubbles are transported by the liquid steel from the vacuum chamber to the snorkel, and escape from the free surface of the ladle finally. (3) There are little CO bubbles in the Ar plume region of the vacuum chamber and the snorkel because CO bubbles are transported to other regions with the influence of strong upward argon stream. 3.5. Carbon distribution during decarburization Fig. 12 gives the similar spatial distribution of carbon mass concentration predicted by different coupling models. (1) The carbon mass concentration near the Ar plume is lower than other regions in the ladle because of the decarburization at the surface of argon bubbles. (2) The carbon mass concentration in the vacuum chamber and the snorkel is lower than that in the ladle because of the
S. Chen et al. / International Journal of Heat and Mass Transfer 146 (2020) 118857
(a) Main longitudinal-section
7
(a) Main longitudinal-section
(b) Free surface of the ladle
(b) Free surface of the ladle
(c) Longitudinal-section of the vacuum chamber and upper part of snorkel
(c) Longitudinal-section of the vacuum chamber and upper part of snorkel
Fig. 5. Liquid steel flow in SSRF at the 5th minute of decarburization (one-way coupling model).
Fig. 6. Liquid steel flow in SSRF at the 5th minute of decarburization (two-way coupling model).
decarburization in the inner sites of vacuum chamber and the decarburization at the free surface of argon bubbles. (3) The carbon mass concentration in the vacuum chamber and the upper part of snorkel is the lowest in SSRF because of the decarburization at the free surface of the vacuum chamber and the flow behavior of the recirculation zones in Figs. 5(c) and 6(c).
Fig. 12 also shows three main differences as follows between the two models. (1) On the base of the one-way coupling model, there is the weak turbulent flow near the free surface of the ladle, and then leads to the limited mass transfer of carbon and oxygen, so the predicted carbon mass concentration near the free surface of ladle is greater than that predicted by the two-way coupling
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Fig. 8. Cross-section planes in the snorkel.
(a) One-way coupling model
Fig. 9. Ratio of Ar plume at the cross-sectional planes in the snorkel.
(b) Two-way coupling model Fig. 7. Spatial distribution of Ar in SSRF at the 5th minute of decarburization.
model. (2) Because the two-way coupling model considers the stirring effect of CO gas, its stronger fluid flow, as shown in Fig. 6, can enhance the mass transfer of carbon in liquid steel. Thus, the predicted carbon mass concentration is less than that predicted by the one-way coupling model. (3) The one-way coupling model does not consider the stirring effect of CO bubbles, such a fact leads to the weaker turbulent flow, as shown in Fig. 5(c), and further limits the mass transfer of carbon and oxygen in these regions, so the carbon mass concentration in the vacuum chamber and the snorkel is greater than that predicted by the two-way coupling model.
Fig. 10. CO generation rate and Ar blowing rate during decarburization.
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9
(a) Carbon mass concentration (one-way coupling model) Fig. 11. Spatial distribution of CO in SSRF at the 5th minute of decarburization (two-way coupling model).
4. Conclusions Based on the Eulerian-Eulerian approach, a two-way coupling model considering CO gas is proposed to have a deep sight into the Ar-CO-liquid steel flow and decarburization process in SSRF. And the effect of CO gas on the flow field of argon gas and liquid steel, the decarburization rate are investigated in detail. The conclusions are summed as follows: (1) During the overall decarburization process, the mole number of CO generated by decarburization is about 3 times the argon mole number blown into the ladle. And the CO generation rate is greater than argon blowing rate at the first 12 min. (2) In comparison with the one-way coupling model, the carbon mass concentration predicted by the two-way coupling model is more consistent with the industrial experimental result, and the maximum carbon mass concentration difference is approximately 10%. (3) The CO gas appears near the free surface of the ladle and in the vacuum chamber and the snorkel. (4) Because of the stirring effect of CO gas, the more complicated flow field can enhance the mass transfer and increase the decarburization rate. And the carbon mass concentration predicted by the two-way coupling model is less than that predicted by the one-way coupling model. (5) The Ar plume area predicted by the two-way coupling model is larger than that predicted by the one-way coupling model, and it is closer to the center line of the snorkel.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China and Shanghai Baosteel (No. U1460108) and National Natural Science Foundation of China (No.51574074).
(b) Carbon mass concentration (two-way coupling model) Fig. 12. Spatial distribution of dissolved carbon in SSRF at the 5th minute of decarburization.
Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118857.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Ar-CO-liquid steel flow with decarburization chemical reaction in single snorkel refining furnace Shifu Chen a,b, Hong Lei a,b,⇑, Meng Wang a,b, Bin Yang a,b, Weixue Dou b,c, Lishan Chang c, Hongwei Zhang a,b a
Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, 110004 Shenyang, China School of Metallurgy, Northeastern University, 110004 Shenyang, China c Jingye Iron and Steel Limited Company, Shijiazhuang 050400, China b
a r t i c l e
i n f o
Article history: Received 23 April 2019 Received in revised form 16 September 2019 Accepted 7 October 2019
Keywords: Single snorkel refining furnace Single snorkel RH Vacuum Ar-CO-liquid steel flow Continuous-flow decarburization reaction Two-way coupling mathematical model
a b s t r a c t As a new style refining equipment developed from the traditional RH furnace, Single Snorkel Refining Furnace (SSRF), which is also called as single snorkel RH, is widely used for producing ultra-low carbon steel. However, the effect of CO gas on fluid flow and decarburization is not reported in the existing literatures. Based on the Eulerian-Eulerian approach, a two-way coupling mathematical model considering CO gas is proposed to investigate the coupling phenomenon of Ar-CO-liquid steel flow and decarburization in SSRF. And the industrial experimental data is employed to validate the numerical result. In comparison with the one-way coupling model, the numerical result predicted by the two-way coupling model is closer to the industrial experimental data. The CO mole number, which is generated by the overall decarburization process, is about 3 times the argon mole number blown into the ladle, and the CO generation rate is greater than argon blowing rate at the first 12 min. Because of the stirring effect of CO gas, there are the more complex fluid flow, the stronger mass transfer, the greater decarburization rate and the lower carbon mass concentration in the liquid steel during decarburization. Besides, the Ar plume area predicted by the two-way coupling model is larger and it is closer to the center line of the snorkel. Therefore, the effect of CO gas on the fluid flow cannot be ignored and the two-way coupling model can describe the metallurgical phenomena in SSRF more precisely. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction During the secondary refining process, RH (Rheinstahl-Heraeus) furnace, which plays a quite vital role in producing high quality steel, is widely applied to remove carbon, oxygen, nitrogen, hydrogen and inclusions in liquid steel. In order to improve the refining effect and promote the productivity, many researchers have proposed many measures in traditional RH furnace, such as increasing the height of the vacuum chamber, changing the diameter and number of the snorkel, introducing multi-function nozzles [1,2]. Single Snorkel Refining Furnace (SSRF), which is also called Single Snorkel RH, is developed by China steel company in the 1970s [3,4]. In SSRF, the up and down snorkels in traditional RH are combined into a large cylindrical snorkel, as shown in Fig. 1, and the argon gas is blown into the liquid steel from the bottom of the ladle. Up to now, many researchers paid attention to the gas liquid flow pattern [1,5–9,13], circulation flow rate [10–13], mixing ⇑ Corresponding author at: Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, 110004 Shenyang, China. E-mail address: [email protected] (H. Lei). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118857 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
phenomenon [13–16], gas volume fraction distribution [13,17,18] and decarburization mechanism [19–25] of traditional RH. But in comparison with traditional RH, only a few of papers focused on the fluid flow and decarburization of SSRF. In order to improve the degassing captivity of DH (Dortmund-Hörder) refining process, Nippon Steel Corporation in Japan transformed DH into REDA (Revolutionary Degassing Activator) to produce ultra-low carbon steel in 1990s [26]. For the fluid flow system, Yang et al. [3] simulated the three-dimensional flow field of liquid steel to optimize the configuration and operation parameters of an 80 t SSRF, and Dai et al. [27] investigated the mixing efficiency and the circulation rate by different injection positions and snorkel diameters in SSRF. By the water model, Rui et al. [28] studied the effect of elliptical snorkel on the decarburization rate in SSRF. You et al. [4] developed a dynamic model, which considered three decarburization sites: argon bubble surface, inner site of the vacuum chamber and free surface of the vacuum chamber. With a one-way coupling mathematical model, Geng et al. [29] investigated the decarburization, the fluid flow and the inclusion collision-aggregation in SSRF. However, some important problems about the modelling of the metallurgical phenomenon in SSRF are far from being solved. During the SSRF decarburization process, a large amount of CO
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Nomenclature A d D ! g h k k/;Ar k/;L K !CO M M p Q r S t ! u
area (m2) diameter (m) diffusion coefficient (m2/s) gravitational acceleration (m/s2) distance (m) turbulent kinetic energy (m2/s2) mass transfer coefficient from liquid steel to bubble surface (m/s) mass transfer coefficient from liquid steel to reaction boundary (m/s) decarburization equilibrium constant momentum transfer (N/m3) molar mass (g/mol) pressure (Pa) circulation flow rate (t/min) radius (m) source term for carbon-oxygen reaction time (s) velocity (m/s)
V
volume (m3)
Greek symbols r interfacial energy (N/m) e turbulent eddy dissipation (m2/s3) a volume fraction b unit conversion coefficient of pressure q density (kg/m3) l viscosity (Pas) w mass concentration w equilibrium mass concentration Subscript / cir eff g l mix
C and O circulation effective gas liquid steel mixing
Fig. 1. Schematic of Single Snorkel Refining Furnace and two-way coupling calculation methodology.
bubbles are generated in the liquid steel. Like argon bubbles, CO bubbles also affect the multiphase flow field, and the related gasliquid system is in an unsteady state because the number of CO bubbles changes with the decarburization time, as shown in Fig. 1. In the meantime, the decarburization rate is also be influenced by the stirring effect of CO bubbles. But all the fluid flow and the decarburization models reported in the existing literatures are one-way coupling models, which do not take into account of the influence of CO bubbles. Based on the Eulerian-Eulerian approach, a two-way coupling mathematical model considering the stirring effect of CO bubbles is proposed to investigate the coupling phenomenon of unsteady argon-CO-liquid steel flow and decarburization in SSRF. Then, the industrial experimental data is applied to validate the mathematical model. Certainly, this paper also shows the effect of CO bubbles on the multiphase flow and the decarburization in detail.
2. Mathematical model Fig. 2 gives the solution methodology of the mathematical model in detail. The two-way coupling mathematical model is carried out to investigate the Ar-CO-liquid flow based on the decarburization chemical reaction in SSRF. Considering the generation of CO gas caused by the carbon and oxygen in the liquid steel, the Eulerian-Eulerian multiphase flow model, the standard k e turbulent model and the interphase momentum transfer model are employed to get the unsteady Ar-CO-liquid steel flow field. And the transport equations of carbon and oxygen and decarburization model are calculated to obtain the instantaneous spatial distribution of CO bubbles. It should be noted that, the behavior of CO bubbles generated by decarburization is an unsteady process, so the effect of CO bubbles on the fluid flow is also an unsteady process.
S. Chen et al. / International Journal of Heat and Mass Transfer 146 (2020) 118857
ll;t ¼ ql C l
k
3
2
ð2Þ
e
Based on the research model proposed by Sato et al. [33,34], the bubble-induced turbulence can be formulated by:
! lg;t ¼ C g;l ql ag dg ! u g u l
ð3Þ
where the model constant C g;l is 0.6. According to Jakobsen et al. [35], the effective viscosity of argon gas and CO gas are determined by the effective viscosity of liquid steel in the multiphase flow.
Fig. 2. Flow chart of the multiphase flow and decarburization by the two-way coupling mathematical model.
lAr;eff ¼
qAr l ql l;eff
ð4Þ
lCO;eff ¼
qCO l ql l;eff
ð5Þ
qAr and qCO are the constant density of argon gas and CO gas, respectively. In the multiphase momentum equations in Table 1, the inter! phase momentum transfer (M ) between the gas phase (argon and CO) and the liquid phase comes from the interfacial forces. As shown in Table 2, the interfacial forces can be divided into five categories: drag force, lift force, virtual mass force, wall lubrication force and turbulent dispersion force [30,36]. For the argon gas blown into SSRF, the initial diameter of argon bubble ðdAr Þ can be formulated by [18,30,31,41]:
Because of the complicated metallurgical phenomenon and the heavy numerical computational load, some assumptions are applied to simplify the mathematical model. (1) The fluid flow in SSRF is not affected by the top slag, there is not any chemical reactions between liquid steel and slag, and the free surfaces of the vacuum chamber and the ladle are flat [9,17,18,23,30,31]. (2) The gas-liquid flow and the decarburization occur at 1873 K in SSRF, and the fluid flow is a Newtonian incompressible viscous flow [9,17,23,30,31]. (3) The interactions (such as breakup and coalescence) among bubbles are neglected, and the bubbles are spheres [9,17,21,30,31]. (4) The chemical reaction between carbon and oxygen in the liquid steel takes place on the bubble surface, the free surface of the vacuum chamber and the inner site of the vacuum chamber [4,18,21,24,25,31]. (5) CO bubbles are generated at once after the chemical reaction between carbon and oxygen occurs, which have a same size as argon bubbles. (6) The argon blowing rate does not change during the SSRF refining process [23–25,27,29–31]. 2.1. Multiphase fluid flow In the current work, the flow fields about argon gas, CO gas and liquid steel are calculated by the multiphase fluid model (EulerianEulerian approach). The related governing equations are summarized in Table 1. The effective viscosity of liquid steel (ll;eff ) consists of three items [33,34]: the molecular viscosity (ll ), the turbulent viscosity (ll;t ) and the bubble-induced turbulence (lg;t ).
ll;eff ¼ ll þ ll;t þ lg;t With:
ð1Þ
dAr ¼ 0:091
rAr ql
0:5 u0:44 Ar;0
ð6Þ
where rAr is the interfacial energy between argon gas and liquid steel, N/m; uAr;0 is the argon blowing velocity determined by the circulation argon flow rate, m/s. According to the research of Tatsuoka et al. [42], under high vacuum environment, the main position for bubbles expansion is near the free surface of vacuum chamber. Therefore, the bubble size is treated as a constant. 2.2. Decarburization process In the SSRF, the decarburization chemical reaction can be expressed as:
½C þ ½O ¼ COðgÞ
ð7Þ
For the decarburization process, the decarburization rate is controlled by the mass transfer of carbon and oxygen in liquid steel [21,25]. And the mass conservation can be formulated by [25]:
@ ! ðq w/ Þ þ r ðql u l w/ Þ ¼ r ðql D/;eff rw/ Þ S/ @t l
ð7Þ
where / denotes C and O; D/;eff is the effective diffusion coefficient, m2/s; S/ is the source term of carbon and oxygen transport equation in the three sites during decarburization. The decarburization rate of three sites is given in Table 3, and the carbon and oxygen mass concentration at equilibrium state are determined by the thermodynamic equation about decarburization chemical reaction. For the decarburization at the vacuum chamber free surface, based on the research of Takahashi et al. [21], the effective decarburization area is 10 times the cross section of the vacuum chamber because of the splash and fluctuation of liquid steel [18,22,31]. For the decarburization at the argon bubbles surface, the mass transfer coefficient k/;Ar can be formulated by [24,31]:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k/;Ar ¼ 2 D/ uslip Ar =pdAr
ð8Þ
where uslip Ar is the slip velocity, m/s; D/ is the diffusion coefficient,
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Table 1 Governing equations of fluid flow. Items
Equations
List of symbols
! @ @t ðqAr aAr Þ þ r qAr aAr u Ar ¼ 0 ! MCO dwC @ @t ðqCO aCO Þ þ r qCO aCO u CO ¼ ql MC dt ! @ @t ðql al Þ þ r ql al u l ¼ 0 ! ! ! @ @t qAr aAr u Ar þ r qAr aAr u Ar u Ar
! ! T ! ! ¼ aAr rp þ r aAr lAr;eff r u Ar þ r u Ar þ qAr aAr g þ M Ar;l ! ! ! @ @t qCO aCO u CO þ r qCO aCO u CO u CO
T ! ! ! ! ¼ aCO rp þ r aCO lCO;eff r u CO þ r u CO þ qCO aCO g þ M CO;l ! ! ! @ @t ql al u l þ r ql al u l u l
! T ! ! ! ! ¼ al rp þ r al ll;eff r u l þ r u l þ ql al g þM l;Ar þ M l;CO
Continuity equation
Momentum equation
! r u l kÞ i ðal ql ll;t ¼ r al ll þ rk r k þ al ðGk ql eÞ þ al ql k
Turbulent kinetic energy equation
@ðal ql kÞ @t hþ
Turbulent eddy dissipation equation
@ðal ql eÞ @t hþ
a is the volume fraction, aAr þ aCO þ al ¼ 1; q is the
! density, kg/m3; u is the velocity, m/s; t is the time, s; M is the molar mass, g/mol; wC is the mass concentration of dissolved carbon.
! g is the gravitational acceleration, m/s2; p is the ! pressure, Pa; leff is the effective viscosity, Pas; M Ar;l and ! M CO;l are the momentum transfer of gas (Ar and CO) !
phase relative to liquid steel, respectively, N/m3; Ml;Ar !
and M l;CO are the momentum transfer of liquid steel relative to gas (Ar and CO), respectively, N/m3.
k is the turbulent kinetic energy, m2/s2; e is the turbulent eddy dissipation, m2/s3; C l ¼ 0:09, C 1 ¼ 1:44, C 2 ¼ 1:92, rk ¼ 1:0, re ¼ 1:3 [13,16,32].
! r u l eÞ i ðal ql ll þ lrl;te r e þ al ke ðC 1 Gk C 2 ql eÞ þ al ql e
¼ r al
Table 2 Interfacial forces model. Items
Equations ! ! ! ! ! F D ¼ 34 CdDg ag ql u g u l u g u l ! ! ! ! F L ¼ C L ag ql u l u g r u l ! ! ! D u F VM ¼ C VM ag ql DlDtu l gDt g
Drag force [37] Lift force [37,38] Virtual Mass Force [18,38] Wall Lubrication Force [39]
! ! ! 2 ! F WL ¼ C WL ag ql u l u g n W
Turbulent Dispersion Force [40]
! mt;l rag ral F TD ¼ C TD C D SC;l ag al
2rCO rCO
C D is the drag force coefficient. C L is the lift force coefficient. C VM is the virtual mass coefficient. ! C WL is the wall lubrication force coefficient; n W is the unit normal vector away from the wall. C TD is the turbulent dispersion force coefficient; mt;l is the turbulent kinematic viscosity of the liquid phase.
DC ¼ 2:24 108 m2 =s and DO ¼ 1:26 108 m2 =s [24,31]. For the decarburization at the inner site of the vacuum chamber, the dissolved carbon and oxygen are at the supersaturated state, and the impact of CO nucleation pressure is considered in the mathematical model. The partial pressure of CO ðPCO Þ can be formulated by [4,18,43]:
PCO ¼ PV þ bql gh þ b
List of symbols
ð9Þ
where PV is the vacuum chamber pressure, Pa; rCO is the interfacial energy, N/m; b is the unit conversion coefficient of pressure.
2.3. Computational conditions Fig. 3 gives the geometric parameters and mesh configuration of SSRF. The computational domain is discretized into 250 000 grids by ICEM CFD. For the nozzle at the bottom of the ladle, the inlet velocity of argon gas is determined by the circulation argon flow rate, and the inlet velocity of CO gas equals zero. Degassing condition is applied at the free surfaces of the vacuum chamber and the ladle through which argon gas and CO gas can escape from the free surface at the terminal floating velocity, but liquid steel cannot. Besides, no slip wall condition is applied to all walls in SSRF. In the vacuum chamber, the pressure is 67 Pa. Physical properties
Table 3 Governing equations of decarburization. Items
Equations
Decarburization rate at the vacuum chamber free surface [18,21,22,31]
dw/1 dt
Decarburization rate at the argon bubbles surface [24,31]
dw/2 dt
Decarburization rate at the inner site of the vacuum chamber [21,31]
dw/3 dt
List of symbols
M/ 10AV h¼ 1000 V min kC;L 1000 MC wC
M/ 1000
i wC ; kO;L 1000 MO wO wO
6aAr AAr pd3Ar
¼ h i 1000 min kC;Ar 1000 MC wC wC ; kO;Ar MO wO wO ¼ k0 hh0 ðK CO wC wO P CO Þ
AV is the cross section area of vacuum chamber, m2; V is the volume of liquid steel, m3; w/ is the equilibrium mass concentration; k/;L is the mass transfer coefficient from liquid steel to reaction boundary, kC;L ¼ 6:0 104 m=s, kO;L ¼ 4:5 104 m=s [24]. k/;Ar is the mass transfer coefficient from liquid steel to bubble surface [24,31]; AAr is the surface area, m2; dAr is the diameter, m. k0 is a constant of 3 107 ð1=Pa sÞ at h0 ¼ 0:15 m [21]; h is the distance from CO bubble to liquid surface, m; K CO is the decarburization equilibrium constant; P CO is the spatial pressure of CO.
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four different grids. The maximum difference about Q cir is only 0.21% and the maximum difference about tmix is only 1.59%. Thus, the 250 000 grids is applied to finish the following calculation in order to reduce the computational load. To validate the mathematical model, two industrial experiments of SSRF decarburization are conducted in a steel company, as shown in Fig. 4. The monitor position of carbon mass concentration in the numerical simulation is consistent with the sampling position in the industrial experiment. During the industrial decarburization process, the liquid steel is sampled every 5 min with the Ultra-low Carbon Sampler, and the spectrum analytical method is used to measure the carbon content in liquid steel. Fig. 4 shows that the predicted carbon mass concentration agrees well with the industrial experimental data. The carbon mass concentration predicted by the two-way coupling model is less than that predicted by the one-way coupling model. For the experiment of wC0 ¼ 225 106 , the error between the one-way coupling model and the industrial experiment is 48.39% and 22.78% at the 5th and 10th minute of decarburization, respectively. But the error between the two-way coupling model and the industrial experiment is 13.71% and 5.06% at the 5th and 10th minute of decarburization, respectively. And for the experiment of
Fig. 3. Geometric parameters and mesh configuration.
Table 4 Physical properties and numerical parameters. Items
Values
Density of liquid steel Viscosity of liquid steel Density of argon gas Density of CO gas Interfacial energy between argon bubble and liquid steel Interfacial energy between CO bubble and liquid steel Circulation argon flow rate Vacuum chamber pressure Initial carbon mass concentration
7000 kg/m3 0.0062 Pas 1.783 kg/m3 1.250 kg/m3 1.5 N/m [24] 1.9 N/m [43] 330 NL/min 67 Pa 225 106
Initial oxygen mass concentration
1135 106
and numerical parameters during the calculation are shown in Table 4. 2.4. Computational procedure In the current work, the computational fluid dynamics software CFX combined with the CFX Expression Language (CEL) is employed to investigate the multiphase flow and decarburization in SSRF. Partial differential equations are solved by the finite volume method. The time scale is 0.01 s and the convergence criteria is that the root-mean-square normalized residual of all variables is less than 105 . By parallel computing on 16 CPU cores, it takes about two weeks to finish a two-way coupling model calculation. 3. Results and discussions 3.1. Model validation To ensure the numerical results quite compelling and persuasive, the verification of grid independence is carried out by a steady flow field calculation. Table 5 gives the circulation flow rate (Q cir ) and the mixing time (tmix ) of liquid steel on the base of
wC0 ¼ 407 106 , the error between the one-way coupling model and the industrial experiment is 5.26%, 28.67% and 15.88% at the 5th, 15th and 25th minute of decarburization, respectively. But the error between the two-way coupling model and the industrial experiment is 4.68%, 7.17% and 3.82%, respectively. Thus, the carbon mass concentration predicted by the two-way coupling model is closer to the industrial results. Furthermore, it can be seen from Fig. 4 that the difference of the predicted carbon mass concentration between the one-way coupling model and the two-way coupling model increases with the increase of the decarburization time. At the 5th minute of decarburization, the difference rises 13.87% to 12:20 106 in the experiment of wC0 ¼ 225 106 and rises 9.62% to 17:32 106 in the experiment of wC0 ¼ 407 106 . As the chemical reaction between carbon and oxygen proceeds further, the difference decreases gradually because fewer CO bubbles are generated in the later stage of decarburization process with the decrease of the carbon and oxygen concentration in liquid steel. Because the equilibrium constant of the chemical reaction between carbon and oxygen is determined by the temperature in liquid steel, the CO bubbles during decarburization can only improve the decarburization kinetic conditions and increase the decarburization rate in SSRF. Therefore, the final equilibrium carbon mass concentration predicted by the twoway coupling model is the same as that predicted by the oneway coupling model. The Ar-CO-liquid steel flow and decarburization in the experiment of wC0 ¼ 225 106 are investigated in detail in the following results and discussions. 3.2. Liquid steel flow field during decarburization Figs. 5 and 6 give the unsteady liquid steel flow fields predicted by the one-way coupling model and the two-way coupling model in SSRF at the 5th minute during decarburization. These flow fields have some similar features. (1) With the help of floating argon bubbles blown from the bottom of the ladle, there is a large recirculation zone in SSRF: ladle -> snorkel -> vacuum chamber -> snorkel -> ladle. (2) A small recirculation zone appears near the free surface of ladle because of the driving effect of argon bubbles. In SSRF gas-liquid system, the two-way coupling model can describe the effect of CO bubbles on liquid steel flow but the one-way coupling model don’t consider the existence of CO bubbles. Thus, Figs. 5 and 6 also give the differences about the fluid flow at the 5th minute. (1) On the side of ladle away from the argon
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Table 5 Verification of grid independence. Items
Q cir , t/min tmix , s
Grids 200 000
250 000
300 000
350 000
33.16 123.92
33.15 124.56
33.09 123.44
33.10 125.40
cross-sectional planes of Ar plume are defined in the snorkel, as shown in Fig. 8. Fig. 9 gives the ratio between the Ar plume area (with the volume fraction of argon greater than 1%) and the cross-sectional plane area. It can be seen from that the difference of Ar plume area between the one-way coupling model and the two-way coupling model increases gradually from the bottom to the upper part of the snorkel. And the maximum Ar plume area ratio predicted by the two-way coupling model is 33.87% of the cross-sectional plane in Fig. 9, which is 2.23 times that predicted by the one-way coupling model. Consequently, the flow behavior of argon bubbles is changed significantly when the CO gas is considered in the two-way coupling model. 3.4. CO distribution during decarburization
Fig. 4. Comparison of predicted carbon mass concentration with the industrial experimental data.
bubbles main stream, there is a recirculation zone near the free surface of the ladle predicted by the two-way coupling model. (2) Near the free surface of the ladle, the fluid velocity predicted by the two-way coupling model is greater than that predicted by the one-way coupling model. (3) In the vacuum chamber and the upper part of snorkel, there are 4 recirculation zones predicted by the two-way coupling model and 2 recirculation zones predicted by the one-way coupling model. (4) In the snorkel, the velocity of liquid steel near the center line predicted by the twoway coupling model is greater than that predicted by the oneway coupling model. These differences come from the fact that the spatial distribution of CO bubbles is different from that of argon bubbles, which will be discussed in Section 3.4. 3.3. Ar distribution during decarburization As the essential factor driving the flow of liquid steel, the upward argon stream in the snorkel plays a crucial role in the multiphase flow and decarburization in SSRF. Fig. 7 shows that Ar plume region expands gradually with the floatation of argon bubbles, and the simulated fluid flow pattern is similar to the water model experiment result [28]. But there are also different features of Ar plume region between the one-way coupling model and the two-way coupling model. (1) In comparison with Fig. 7(b), the Ar plume region predicted by the one-way coupling model is narrow relatively, but the Ar plume region predicted by the two-way coupling model is wider due to the more recirculation zones and stronger turbulent flow in the vacuum chamber and the snorkel. (2) On the base of the one-way coupling model, most of argon bubbles are close to the snorkel wall, and a few argon bubbles escape from the liquid steel from the free surface of the ladle. But on the base of the two-way coupling model, the Ar plume region is closer to the center line of the snorkel, and there are only a few argon bubbles closing to the snorkel wall. In order to give the difference about the spatial distribution of argon predicted by different coupling models more intuitively, four
Fig. 10 shows the significant difference between CO generation rate and argon blowing rate predicted by two-way coupling model in SSRF. As the chemical reaction between carbon and oxygen proceeds, the carbon mass concentration decreases and CO generation rate slows down gradually during decarburization process. The maximum CO generation rate is 270.10 mol/min at the 1st minute, which is 18.33 times the argon blowing rate (14.73 mol/min). After the 12th minute, the CO generation rate is less than argon blowing rate. And the CO generation rate is 3.08 mol/min at the 20th minute. There are two interesting phenomena in Fig. 10. (1) CO generation rate is greater than the argon blowing rate at the first 12 min. (2) The amount of CO mole number is 991.52 mol, which is 3.37 times the argon mole number blown from the bottom of the ladle. Thus, the multiphase flow should consider both CO gas and argon gas during SSRF decarburization. Fig. 11 gives the spatial distribution of CO bubbles in SSRF at the 5th minute of decarburization predicted by the two-way coupling model. Most of CO bubbles appear near the free surface of the ladle and in the vacuum chamber and the snorkel. And the spatial distribution of CO bubbles corresponds with the recirculation zones near the free surface of the ladle and in the vacuum chamber and the snorkel, as shown in Fig. 6(a) and (c). Several reasons lead to such interesting phenomena. (1) In the current mathematical model, CO bubbles are generated at once after the chemical reaction between carbon and oxygen occurs. (2) As one important decarburization site, many CO bubbles are generated in the inner sites of the vacuum chamber, some CO bubbles escape from the free surface of the vacuum chamber directly, and other CO bubbles are transported by the liquid steel from the vacuum chamber to the snorkel, and escape from the free surface of the ladle finally. (3) There are little CO bubbles in the Ar plume region of the vacuum chamber and the snorkel because CO bubbles are transported to other regions with the influence of strong upward argon stream. 3.5. Carbon distribution during decarburization Fig. 12 gives the similar spatial distribution of carbon mass concentration predicted by different coupling models. (1) The carbon mass concentration near the Ar plume is lower than other regions in the ladle because of the decarburization at the surface of argon bubbles. (2) The carbon mass concentration in the vacuum chamber and the snorkel is lower than that in the ladle because of the
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(a) Main longitudinal-section
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(a) Main longitudinal-section
(b) Free surface of the ladle
(b) Free surface of the ladle
(c) Longitudinal-section of the vacuum chamber and upper part of snorkel
(c) Longitudinal-section of the vacuum chamber and upper part of snorkel
Fig. 5. Liquid steel flow in SSRF at the 5th minute of decarburization (one-way coupling model).
Fig. 6. Liquid steel flow in SSRF at the 5th minute of decarburization (two-way coupling model).
decarburization in the inner sites of vacuum chamber and the decarburization at the free surface of argon bubbles. (3) The carbon mass concentration in the vacuum chamber and the upper part of snorkel is the lowest in SSRF because of the decarburization at the free surface of the vacuum chamber and the flow behavior of the recirculation zones in Figs. 5(c) and 6(c).
Fig. 12 also shows three main differences as follows between the two models. (1) On the base of the one-way coupling model, there is the weak turbulent flow near the free surface of the ladle, and then leads to the limited mass transfer of carbon and oxygen, so the predicted carbon mass concentration near the free surface of ladle is greater than that predicted by the two-way coupling
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Fig. 8. Cross-section planes in the snorkel.
(a) One-way coupling model
Fig. 9. Ratio of Ar plume at the cross-sectional planes in the snorkel.
(b) Two-way coupling model Fig. 7. Spatial distribution of Ar in SSRF at the 5th minute of decarburization.
model. (2) Because the two-way coupling model considers the stirring effect of CO gas, its stronger fluid flow, as shown in Fig. 6, can enhance the mass transfer of carbon in liquid steel. Thus, the predicted carbon mass concentration is less than that predicted by the one-way coupling model. (3) The one-way coupling model does not consider the stirring effect of CO bubbles, such a fact leads to the weaker turbulent flow, as shown in Fig. 5(c), and further limits the mass transfer of carbon and oxygen in these regions, so the carbon mass concentration in the vacuum chamber and the snorkel is greater than that predicted by the two-way coupling model.
Fig. 10. CO generation rate and Ar blowing rate during decarburization.
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(a) Carbon mass concentration (one-way coupling model) Fig. 11. Spatial distribution of CO in SSRF at the 5th minute of decarburization (two-way coupling model).
4. Conclusions Based on the Eulerian-Eulerian approach, a two-way coupling model considering CO gas is proposed to have a deep sight into the Ar-CO-liquid steel flow and decarburization process in SSRF. And the effect of CO gas on the flow field of argon gas and liquid steel, the decarburization rate are investigated in detail. The conclusions are summed as follows: (1) During the overall decarburization process, the mole number of CO generated by decarburization is about 3 times the argon mole number blown into the ladle. And the CO generation rate is greater than argon blowing rate at the first 12 min. (2) In comparison with the one-way coupling model, the carbon mass concentration predicted by the two-way coupling model is more consistent with the industrial experimental result, and the maximum carbon mass concentration difference is approximately 10%. (3) The CO gas appears near the free surface of the ladle and in the vacuum chamber and the snorkel. (4) Because of the stirring effect of CO gas, the more complicated flow field can enhance the mass transfer and increase the decarburization rate. And the carbon mass concentration predicted by the two-way coupling model is less than that predicted by the one-way coupling model. (5) The Ar plume area predicted by the two-way coupling model is larger than that predicted by the one-way coupling model, and it is closer to the center line of the snorkel.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China and Shanghai Baosteel (No. U1460108) and National Natural Science Foundation of China (No.51574074).
(b) Carbon mass concentration (two-way coupling model) Fig. 12. Spatial distribution of dissolved carbon in SSRF at the 5th minute of decarburization.
Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118857.
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