J. of Supercritical Fluids 65 (2012) 25–31

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2D and 3D CFD modelling of a reactive turbulent flow in a double shell supercritical water oxidation reactor S. Moussiere a , A. Roubaud a,∗ , O. Boutin b , P. Guichardon b , B. Fournel a , C. Joussot-Dubien a a b

CEA, DEN, Supercritical and Decontamination Processes Laboratory, BP 17171, 30207 Bagnols/Cèze Cedex, France Aix Marseille Université, M2P2, UMR CNRS 7340, BP 80, Europôle de l’Arbois, 13545 Aix en Provence, France

a r t i c l e

i n f o

Article history: Received 31 January 2011 Received in revised form 10 February 2012 Accepted 13 February 2012 Keywords: Supercritical water oxidation CFD modelling EDC combustion model Heat transfer Turbulence model Sliding mesh model

a b s t r a c t In order to design and define appropriate dimensions for a supercritical oxidation reactor, a comparative 2D and 3D simulation of the fluid dynamics and heat transfer during an oxidation process has been performed. The solver used is a commercial code, Fluent 6.2® . The turbulent flow field in the reactor, created by the stirrer, is taken into account with a k–␻ model and a swirl imposed to the fluid. In the 3D case the rotation of the stirrer can be modelled using the sliding mesh model and the moving reference frame model. This work allows comparing 2D and 3D velocity and heat transfer calculations. The predicted values (mainly species concentrations and temperature profiles) are of the same order in both cases. The reactivity of the system is taken into account with a classical Eddy Dissipation Concept combustion model. Comparisons with experimental temperature measurements validate the ability of the CFD modelling to simulate the supercritical water oxidation reactive medium. Results indicate that the flow can be considered as plug flow-like and that heat transfer is strongly enhanced by the stirring. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Supercritical water oxidation is an efficient process to treat organic liquid wastes. This technology uses the properties of supercritical water (P > 22.1 MPa and T > 374 ◦ C) to achieve a good mixing between water, oxygen and organic wastes. Typically, the oxidation reaction is fast and complete. Nevertheless, the salt contained in the waste can precipitate in supercritical water due to the low dielectric constant of water (above the critical point, a low value of 5 compared to 80 in liquid water) [1–3]. Moreover, the presence of various complex compounds in the waste with heteroatoms like chlorine, phosphorus or sulphur, forms acids. Coupled to the high temperature, these species lead to the corrosion of materials [4] or inefficient continuous treatment [5–7]. A double shell reactor has been developed in order to overcome both problems. This reactor has been highly effective for treating organic waste containing 100 g L−1 of chlorine and 50% (w/w) of salts with a treatment capacity of 0.2 kg h−1 of pure organics [8]. The overall objective of this work is to define the reactor design to reach a treatment capacity ten times larger, with a double shell stirred reactor, taking into account the safety constraint of radioactive waste management. The major issues are on the length of the reactor, limited to 1 m and

∗ Corresponding author. Present address: CEA Grenoble, DRT/LITEN/DTBH/LTB, Bât. M30, Biomass Technologies Laboratory, 17, rue des martyrs, 38054 Grenoble Cedex 9, France. Tel.: +33 4 38 78 04 54. E-mail address: [email protected] (A. Roubaud). 0896-8446/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2012.02.019

hence on the heat power needed to reach the critical point with a limited exchange surface. 2D and 3D simulations of heat transfer and fluid flows are used as an optimization tool. The specific aim of this study is to simulate the complex reactive flow in the stirred double shell reactor in order to understand the whole phenomenon which leads to an oxidation yield of up to 99.99%. A major parameter in this process is the temperature inside the reactor. For this purpose the heat transfer in the reactor is investigated. The first step is the simulation of the hydrodynamics in the reactor and the second step is the introduction of the oxidation reaction. The numerical simulation of the fluid dynamic has been done using commercial CFD software (Fluent 6.2® ). The validation of the reactor functioning will help in the future to design a reactor with a higher capacity.

2. Materials and methods 2.1. Experimental set-up Fig. 1 shows the flow sheet of the process with the stirred double shell reactor. The external vessel is made of type 316 Stainless Steel and can withstand pressure. The titanium inner tube confines the aggressive species. Air and water are mixed and enter the reactor through the cold zone (right part of the reactor, in blue in Fig. 1). This mixture flows in the annular space where it is pre-heated by the four electric heaters (PR1, PR2, PR3, and PR4, in red in Fig. 1) and by the heat of the reaction coming from the inner part. Organic

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Nomenclature EDC k MRF SMM T TOC u, ui , uj xi , xj

Eddy Dissipation Concept turbulent kinetic energy per unit mass (J kg−1 ) moving reference frame sliding mesh model temperature (K) total organic carbon (g L−1 ) velocity, xi velocity, xj velocity (m/s) axis coordinates

Greek letters ˛ constant ε dissipation rate of turbulence kinetic energy (m2 s−3 )  organic air equivalence ratio (defined as (oxidant to fuel ratio/stoichiometric oxidant to fuel ratio))  fluid density (kg m−3 ) turbulent dynamic viscosity (kg m−1 s−1 ) t ˜ turbulent kinematic viscosity (m2 s−1 ) ω specific dissipation rate (s−1 ) ωR stirrer rotation speed (rpm) Constant values k–␧ model C , C1 , C2 , ˛ε , ˛k k–␻ model C , ˛*, *, , S, ˇ*, ˇ Spalart–Allmaras model C1

Fig. 2. Temperature measurements during methanol degradation versus distance x from the injection (m).

placed in the waste injection tube in the hot zone. Three other thermocouples are placed along the titanium inner tube. The last thermocouple is placed at the outlet of the reactor. The experimental conditions and destruction efficiency results are summed up in Table 1. The destruction efficiency is the ratio between the TOC of the liquid phase at the exit of the reactor upon the initial TOC of the waste. The temperature measurements during methanol oxidation runs are taken to validate the numerical calculation. The different experimental profiles used for the comparison with simulation results are presented in Fig. 2. 2.2. Numerical method

compounds are injected in the hot zone inside the inner tube where they mix with the air/water flow. The initiation of the oxidation reactions takes place instantaneously. In the second part of the reactor, the flux is cooled by the cooling jackets and by the air/water mixture flowing in the annular space. Salts are dissolved at the end of the reactor in the colder area. In addition, the stirrer keeps particles in suspension and improves mixing and heat transfer. At the outlet, the effluent is depressurised through a back pressure regulator and separated in two phases. The aqueous phase is analysed by a total organic carbon analyser (TOC) and the gaseous phase is analyzed by a CO, CO2 and O2 on-line gas analyser. The experimental conditions are defined by the equivalence ratio , air, water and organic waste mass flows, the ratio between organic and water mass flows, the reactor temperature and pressure. During the experiments, the reactor temperature is measured by 5 thermocouples, as shown in Fig. 3. A first thermocouple is

Fig. 1. Flowsheet of SCWO process. (For interpretation of the references to color in the text, the reader is referred to the web version of the article.)

The complex geometry of the reactor has been first built in a 2-dimensional axis-symmetric pattern. Considering the system as an incompressible fluid is the strongest hypothesis needed, though a supercritical fluid is usually considered as a compressible fluid. Nevertheless, the fluid flow rate is lower by far than sound speed in the medium. The Mach number defined by the ratio of the fluid velocity over the sound speed is lower than 0.1. So, the compressibility effects can be neglected and the variation of gas density with pressure can be ignored in the flow modelling. All reactions and fluid evolutions are considered to be isobaric at 30 MPa. In fact, a pressure drop of 1 MPa is observed in the reactor, 30 MPa being the pressure at the exit of the reactor, used for the process regulation. This pressure drop does not significantly affect the values of the different physical properties. The standard enthalpies of each species are calculated at 30 MPa using a thermo-chemical cycle. Ideal mixing is assumed and density, viscosity, thermal conductivity and specific heat of mixing are calculated by weighted means. The values of the different properties of the pure components are calculated separately using NIST database and Prophy

Fig. 3. 2D Geometric description of the different zones near the organic injection tube.

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Table 1 Main experimental parameters for methanol degradation. Exp.

Methanol/water ratio (%w)



Water flow rate (kg h−1 )

Methanol flow rate (kg h−1 )

Heaters temperature PR1–PR2–PR3–PR4 (K)

Destruction efficiency (%)

1 2 3

6.24 6.27 7

1.41 1.26 1

2.26 2.07 2.26

0.141 0.130 0.159

680–723–685–562 693–726–686–561 656–682–693–564

99.98 99.95 81.47

Plus software (Prosim, France). The values are calculated in function of temperature, tabulated and then introduced in Fluent® software. The heat transfer coefficient between the fluid and the inner wall of the reactor is computed by Fluent® software using a standard wall function. Fluent® solves the classical mass, momentum and energy conservation equations to describe the fluid behaviour and properties. For the 2D simulation, to simulate the rotation of the stirrer, it is easier to impose a swirl velocity to the fluid instead of using a moving mesh. For this modelling approach, the frame of reference is attached to the moving domain and the governing equations are modified to account for moving frame. To follow the motion, topology of the mesh does not need to be updated, the flow variables being interpolated across a sliding interface. Fig. 3 gives a description of the different zones needed for the 2D mesh construction with 230,000 cells. The blade’s zone is depicted like a fluid. Indeed, it is impossible to depict a solid zone for a blade as it is not solid on all the section. So a fluid zone is implemented as wide as the width of the blades in which a fluid operating speed (or swirl velocity) is set. The swirl velocity uz is set to 2 ωR . ωR is the stirrer rotation speed. This method allows the simulation of the motion imposed to the fluid by the stirrer. In the same way, an operating speed is set for the three holes in the head of the stirrer. For the 3D hexahedral mesh construction, the z direction allows to take into account the design of the stirrer head at 90◦ relatively to the drawing of Fig. 3 with its rectangular hole and its chamfered edge. A description of the stirrer blades is given in Fig. 4. The blades are drawn in blue and the flowing zones are in red. A hole has been drilled in order to enhance the flow. 1,100,000 cells are needed to fully describe the inner geometry. In 3D, two numerical methods are available to simulate the stirrer motion. With the moving reference frame (MRF) method, a rotation speed is imposed to the moving fluid zone and to the solid zone of the stirrer. The fluid velocity is then calculated relating to the moving reference frame of the stirrer. In the sliding mesh method (SMM), only the mesh of the stirrer is moving with its own rotation speed, sliding relatively to the adjacent non moving mesh. The calculation is then transient. Various turbulence models have been investigated in order to simulate hydrodynamics in the reactor. Three turbulence models have been tested in 2D: • The RNG k–␧ turbulence model [9].

• The k–␻ turbulence model [10]. • The Spalart–Allmaras turbulence model [11]. The RNG k–␧ model is based on the standard k–␧ model with application of the renormalization group method [10]. It defines t the turbulent dynamic viscosity as: t =

C k¯ 2 ε¯

(1)

Two equations are needed: one to compute the turbulent kinetic energy k and one to compute the dissipation rate ε. The different constants are given in Table 2. ∂k¯ ∂k¯ + ui = t ∂t ∂xi



∂ui ∂ui + ∂xj ∂xj

∂ε¯ ∂ε¯ ε¯ = C1 t + ui ∂t ∂xi k¯





∂ui ∂ −ε+ ∂xi ∂xi



∂ui ∂ui + ∂xj ∂xj



˛k t

∂k¯ ∂xi

∂ ∂ui ε¯ 2 − C2 + ¯k ∂xi ∂xi





(2)

∂k¯ ˛˛ t ∂xi



(3) In the k–␻ model, a characteristic frequency ω is defined as: ω=

ε C k

(4)

Two equations are needed to calculate k and ω. ∂ ∂(k) ∂(kui ) = + ∂xi ∂xj ∂t



∂(ω) ∂ ∂(ωui ) = + ∂t ∂xi ∂xj

( +  ∗ t )

 ( + t )

∂k ∂xj ∂ω ∂xj



+ t S 2 − ˇ∗ ωk

(5)

˛ω 2 S − ˇω2 k

(6)

 +

The turbulent viscosity is than calculated. t =

˛∗ k ω

(7)

The different constants of this model can be calculated taking into account the Reynolds number value. These calculations can be found in Wilcox [10]. The Spalart–Allmaras uses only one equation for the computation of ˜ , the turbulent kinematic viscosity. t is then defined as: t = ˜vfv1 with fv1 =

(˜v/v)

3

(8)

3

(˜v/v) + Cv31

It then requires less computing time. According to the turbulence model used, the velocity profile is significantly different near the wall, as presented in Fig. 5. The Spalart–Allmaras model gives

Table 2 Constants used in the RNG k–␧ model. Fig. 4. Drawing of the different mesh zones in the y–z plane for the stirrer and the fluid in the inner tube. (For interpretation of the references to color in the text, the reader is referred to the web version of the article.)

C

C1

C2

˛ε

˛

0.009

1.44

1.92

1.3

1

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Fig. 5. Velocity profile at x = 0.25 m inside the inner tube, y radial position (2D case).

a velocity between the blade and the wall equal to the blade tip speed. The velocity abruptly decreases near the wall. Velocity profiles simulated with the k–␻ model and the RNG k–␧ model are quite similar. The velocity progressively decreases from the blade tip to the wall. The RNG k–␧ and the k–␻ turbulence model seem to give a more realistic velocity gradient at the wall, which has also been shown in the published literature [12]. In addition, this has been observed in our previous paper on the 2D simulation of the simple tubular reactor [13]. For the 3D calculations the RNG k–␧ turbulence model has been used due to its better stability in the sliding mesh case, with a mesh pattern of more than one million cells.

The oxidation reaction has been taken into account using the Eddy Dissipation Concept (EDC) combustion model. In this model developed by Magnussen [16], reaction rates are controlled by the mixing of reactants at a molecular scale. This mixing is hence strongly linked with the turbulence intensity of the flow. The use of the EDC combustion model has previously been validated in the case of our tubular reactor for the oxidation of dodecane in supercritical water [13]. Results in terms of wall temperature, locus of reaction and height of the temperature peak inside the reactor were compared for the EDC combustion model and using an Arrhenius law. The EDC model used to compute the mean reaction time predicted more accurately the temperature peak and hence the reaction rate; the latter being controlled by the molecular mixing rather than by the chemical kinetics. The EDC model has been then used in this case of a double shell stirred reactor. The methanol chemical oxidation mechanism chosen take place in two steps:

CO + (1/2)O2 → CO2

motion induces a rotation of the fluid and the maximum velocity is at the blade tip. However the velocity gradient for a given radius is higher with the SMM method than with the MRF. The calculated fluid velocity is identical to the stirrer speed. As shown in Fig. 7 a velocity reduction is observed near the wall. The MRF method is not able to describe the impact of the stirrer blades on the fluid motion excepted for the mean velocity already known. In the same manner, the MRF method is not able to simulate the influence of the wall. Any velocity reduction near the wall is predicted. 3.2. 2D/3D comparison

2.3. Reaction modelling

CH3 OH + O2 → CO + 2H2 O

Fig. 6. Velocity vector coloured by velocity magnitude (m/s), calculated with the MRF method, y–z cross section at x = 0.2 m.

It is worthwhile comparing 2D and 3D models. If the 2dimensional model predictions are as accurate as the 3D model, as significant amount of time may be saved in running the programs to predict reactor temperatures. Figs. 8 and 9 represent the 3D-SMM and 2D calculation results for the fluid velocity in the same region of the stirrer head near the injection and the three holes. In 2D the maximum velocity is equal to the applied swirl velocity to the fluid, which is also equal to the maximum velocity in the 3D-MRF case. This predicted velocity is slightly higher at the 3 holes exit than for the 3D-SMM. The injection velocity is the same but only the 3D calculation is able to predict the main y direction in the first hole compared to the z direction in the 2D case. This z direction is due to the swirl velocity imposed to the fluid in the 2D case. The 3D-SMM method

(9) (10)

Those two equations allow the observation of the formation of CO as an intermediate species. 3. Results and discussion 3.1. 3D calculations Figs. 6 and 7 allow comparing the two numerical methods, MRF and SMM, in the case of the velocity prediction in a cross section, at x = 0.2 m from the injection. This is the region where the initiation of oxidation reactions takes place, just behind the stirrer head. The rotation speed of the stirrer is 300 rpm. In both cases, the stirrer

Fig. 7. Velocity vector coloured by velocity magnitude (m/s), calculated with the SMM method, y–z cross section at x = 0.2 m.

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Fig. 8. Velocity vector coloured by velocity magnitude (m/s), calculated with the SMM method, 3D case.

gives then a more refined description of the influence of the stirrer motion on the fluid dynamic in our supercritical water reactor. 3.3. Heat transfer The simulation obtained previously in 2D, using the RNG k–␻ turbulence model, is compared to the simulation of the reactor in the same conditions, setting a swirl velocity of 0. Fig. 10 shows the temperature fields for both simulations. A homogenization of the temperature field with an operating speed of 31 rad/s is noticeable. Thereby, in the simulated conditions, a temperature of 350 K is obtained in the inner tube at 700 mm from the injection whereas the same temperature is observed at 1000 mm without stirring (see Fig. 10(a) and (b)). Moreover, outlet temperature decreases from 334 to 316 K when the operating speed ranges from 0 to 31 rad/s. The same temperature profiles are obtained with the 2D and the 3D calculations (see Fig. 11). It is possible, with a 2D axis-symmetric pattern, to take into account and estimate the enhancement of heat transfer due to the stirring using a swirl applied on the flow velocity. The first stirrer function is to provide a rapid mixing between the organic and the water/air supercritical mixture but also to enhance heat transfer as the key process parameter is the reactor temperature. Regarding the process design the inner reactor flow regime can be considered as a plug flow-like. Indeed, the different gradients of temperature indicate a stratified progression of temperature, closer to a plug flow functioning rather than a perfectly mixed reactor functioning. In the case of a non reactive run three temperatures have been measured: the injection temperature (Tinj at 58.5 mm from the left side of the reactor), T1 (at 211 mm) and the exit temperature (Ts at

Fig. 10. Temperature (K) field in the reactor (a) without stirring and (b) with stirring.

Fig. 11. Temperature prediction along the reactor with the 3 numerical methods.

1024 mm). Results are condensed in Table 3. For all the calculation cases the temperature is over predicted in the hot region (injection and T1 ) and correctly estimated at the exhaust. The temperature deviations are of the same order, between 13 and 20% in the worse Table 3 Temperature predictions with the different methods and experimental values.

Fig. 9. Velocity vector coloured by velocity magnitude (m/s), calculated in 2D.

Experiment 2D RNG k–␧ Deviation (%) 2D k–␻ Deviation (%) 3D-MRF Deviation (%) 3D-SMM Deviation (%)

Tinj (K)

T1 (K)

Ts (K)

558 670 20.1 634 13.6 640 14.7 641 14.8

603 698 15.8 693 14.9 690 14.4 691 14.6

315 312 0.1 314 0.03 307 −2.5 308 −2.2

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Fig. 12. Temperature profiles versus distance from the injection (m) predicted with the EDC model for methanol oxidation in the case of experiment 1.

case, 15.3% in average. This error seems not to be due to a particular numerical method (2 or 3D) or to the turbulence model. The calculated temperatures are more representative of the heaters 1 and 2 values (1: 703 K, 2: 691 K) than the experimental one measured inside. The calculated heat transfer is then very fast and with very few losses. But in the experimental set up, the flow in the annular zone is a biphasic mixture, due to a lower temperature before entering in the inner tube. Then, the heat transfer is lower than in a homogeneous medium. Similar observations have already been noticed by Bermejo et al. In their work [14], the simulated temperature profile in the transpiring wall reactor is overpredicted by 15%. In their last paper [15], they also observed that heat transfer are not well modelled due to the calculation method of the mixture heat capacity by weight means of pure compounds heat capacities and also due to the hypothesis of a monophasic flow in some regions.

Fig. 13. Temperature profiles versus distance from the injection (m) predicted with the EDC model (solid line) for methanol oxidation, comparison with the measured temperatures (points) for experiment 1.

Fig. 14. Methanol mass fraction near the injection tube for experiment 1 (see Table 1).

3.4. Oxidation Taking into account the results of hydrodynamics and heat transfer parts of this study, the reactive calculations have been done in 2D, less computer time consuming, with a sufficient mixing representation; the 3D calculations not giving a better temperature prediction. It can be seen in Fig. 12 that the predicted temperatures are again overpredicted by 15% against the experimental data. But if a correction is applied on the temperature wall in order to take into account this overprediction, as stated in Section 3.3, a good prediction of the inner temperature is obtained, even in the reactive zone. A temperature reduction due to wall effects has thus been taken into account. Fig. 13 presents the results for methanol oxidation. Those results allow us to validate the methodology of hydrothermal oxidation simulation in the reactor with Fluent® . This combustion simulation provides a view inside the reactor on the methanol consumption (Fig. 14) and the CO production

Fig. 15. CO mass fraction near the injection tube for experiment 1 (see Table 1).

(Fig. 15). The reactive zone is mainly located in the stirrer head. The temperature distribution picture (Fig. 16) shows two higher temperature zones. The first one is located near the injection tube where the CO mass fraction is the highest and the second one after the stirrer head when CO is further oxidised.

Fig. 16. Temperature (K) distribution along the reactor for experiment 1 (see Table 1).

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4. Conclusions

Acknowledgement

In this work, a CFD simulation of a supercritical water oxidation reactor is achieved. All the simulation results were compared with experimental temperature measurement acquired on the 200 g/h pilot POSCEA2. In a first approach, the complex geometry of the reactor has been built in a 2-dimensional axis-symmetric mesh. The stirrer motion is taken into account by imposing a swirl to the fluid. In this case, three various turbulence models have been tested. In order to have a more precise prediction of the fluid flow, a 3-dimensional mesh of the reactor has been built to fully describe fluid dynamics and heat transfer during the oxidation. The rotation of the stirrer has been modelled using the sliding mesh method (SMM). Results were compared to the 2D multi reference frame model. The SMM results are more realistic than the moving reference frame (MRF) method regarding the fluid velocity prediction, the influence of the stirring and the wall effect. The MRF method is comparable to the 2D one with a swirl imposed to the fluid. This work allows also comparing 2D and 3D velocity and heat transfer calculations. Regarding the velocity field prediction in the stirrer head near the injection, the 3D-SMM method gives more realistic details, like the flow direction, than the 2D swirl and the 2D calculation gives a slightly higher maximum velocity. The predicted temperatures are of the same order in both cases with a 15% overprediction compared to the experimental value in the hot zone. Calculated heat transfer is probably overestimated. A wall temperature reduction in the heater section is applied for the EDC simulation of the methanol oxidation. This allows a good representation of the temperature profile. This CFD simulation work confirms that the flow regime inside the reactor is of plug flow type. Heat transfer is improved by the stirrer rotation. 2D calculations are sufficient to predict the reactor temperature fields. The oxidation phenomenon can be modelled using a combustion model as the EDC model, with which the reaction rate is limited by the reactant mixing relatively to the turbulence scales and intensity. The main reactive zones are in the stirrer head and just behind the first stirrer disc. This numerical simulation of the fluid dynamics, heat transfer and oxidation in the double shell stirred reactor, validated on experimental data, allows us to design with a greater degree of confidence an up-scaled new reactor for larger treatment capacity. According to the results obtained, the temperature fields, velocity and oxidation localisation can be predicted.

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