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Numerical simulations of the IPPE target geometry flows
Fusion Engineering and Design 88 (2013) 800–803
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical simulations of the IPPE target geometry flows Akshay Prakash a,∗ , Sotiris Kakarantzas b , Davide Bernardi c , Gioacchino Micciche c , Vincent Massaut d , Bernard Knaepen a a
University Libre de Bruxelles, Belgium University of Thessaly, Volos, Greece EURATOM-ENEA, Brasimore, Italy d SCK-CEN, Mol, Belgium b c
h i g h l i g h t s
We performed numerical simulation of flow over IPPE geometry using turbulence models in FLUENT. Stable free surface profile well within the required design limits was predicted by the models. Velocity profiles across the liquid jet and jet thickness different for different models. There were some 3D effects noticeable for the velocity profiles but the predicted jet thickness similar to 2D models. TKE predicted by different models close to each other and compare will with published data.
a r t i c l e
i n f o
Article history: Received 14 September 2012 Received in revised form 28 January 2013 Accepted 18 February 2013 Available online 11 April 2013 Keywords: IFMIF IPPE Li flow Turbulence Free-surface Curved surface flows
a b s t r a c t A high speed water and liquid lithium (Li) flow is computed over the IPPE geometry to evaluate the performance of different turbulence models in 2D and 3D simulations. Results reported are the thickness of the liquid jet, irregularities in the surface, transient phenomena at the wall which can affect fluid surface and effect of the variation in bulk velocity on these quantities. All models show good near wall resolution of the boundary layer and expected profiles for the free surface flow. Predicted turbulent kinetic energy compare well with published data. Fluctuations of the flow surface at the control location (center of the curved section) and elsewhere are well within 1 mm for all models. However it was observed that the predictions are strongly dependent on the model used. Overall, the predictions of RANS models are close to each other whereas predictions of laminar simulations are close to those obtained with LES models. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The purpose of the International Fusion Materials Irradiation Facility (IFMIF) is to test and qualify materials that can be operated at high temperatures and under intense (neutron) radiation, conditions typical of nuclear fusion devices. In IFMIF, the material samples will be exposed to an intense neutron flux created by bombarding a free surface liquid lithium flow by a dual deuteron beam. A high speed liquid lithium (Li) flow is required to rapidly and continuously evacuate the heat deposited by the two deuterium beams. To test the conceptual design of IFMIF various mock up experiments and simulations on geometries similar to IFMIF were performed. In particular, Gordeev et al. [1,2] studied the effect of unsteady
∗ Corresponding author. Tel.: +32 488134295. E-mail addresses: [email protected], akshay [email protected] (A. Prakash). 0920-3796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.02.106
structures generated by nozzle and straighteners on the free surface and suggested the use of entirely curved backsurface for the facility. Ida et al. [3] have focused on evaluating performance of IFMIF in case of backplate deformation. IPPE (Institute for Physics and Power Engineering) test case [4] is a similar setup where effect of geometrical design and inflow parameters were tested for their effects on the surface stability of the flow. Water was used as the liquid medium. The focus of this paper is on the numerical simulation of water and Li flow for the IPPE geometry. In order to perform high fidelity simulations efficiently, an understanding of various turbulence models on their suitability to reproduce the crucial parameters of the flow discussed below, is required. In order to assess this question, we perform CFD simulations in the turbulent regime where instabilities occurring at the surface of the flow and on the backplate can lead to strong fluctuations of the flow surface. Given the high level of turbulence, several modeling strategies are adopted. First, we use standard RANS modeling and compare the predictions of different models like k–ε, SST and RSM
A. Prakash et al. / Fusion Engineering and Design 88 (2013) 800–803 Table 1 Turbulence models used with their abbreviations. Model
Abbr.
Laminar Navier Stokes Realizable k–ε Shear Stress model Reynolds Stress model Large Eddy Simulation-Smagorinsky subgrid model Large Eddy Simulation-WALE subgrid model Large Eddy Simulations-kinetic energy transport subgrid model 3D LES WALE
Laminar RKE SST RSM LES smag LES wale LES ket 3D
(see Table 1). We also perform some more detailed large-eddy simulations in which the transient properties of large-scale eddies are completely captured while the small-scale turbulence is taken into account through the Smagorinsky or WALE models. A combination of the volume of fluid and level set approaches was used for 2D simulations while for 3D simulations only the volume of fluid method is considered to model the free surface of liquid. Simulations are done with Fluent using default parameters for the turbulence models. The results presented contain velocity profiles on the backplate, the surface structures, the turbulence kinetic energies and the thickness of the flow at different downstream locations. As a parametric analysis of the influence of the average bulk velocity on these flow quantities, simulations were done for bulk velocity of 16 m/s (except for one case where the bulk velocity is 20 m/s).
801
through the SIMPLE scheme. Various turbulence models available in Fluent were used to simulate turbulence: realizable k–ε, Shear Stress Transport (SST), Reynold’s Stress and LES models. k–ε is good for high Reynolds number flows and should predict results with good accuracy away from the wall. SST model combines the k–ε model for flow away from the wall and k–ω model for near wall computations using a blending function. Reynolds Stress model is supposedly the most accurate of the RANS models, solving each of the Reynolds stresses separately (in all 5 additional equations in addition to N–S compared to 2 additional equations for k–ε and k–ω models). LES models are the most computationally intensive models and in theory capture unsteady eddies that can cause perturbations on the free surface. However, they need a fine grid for good resolution. The Smagorinsky subgrid model is known to perform well away from the wall while the WALE model has a better wall behavior. The reader should note that these observations are based on ideas generally accepted in the CFD community and mentioned explicitly in ANSYS Fluent’s manual.
2. Simulation models and boundary conditions The Navier Stokes (N–S) equations are solved using second order spatial and temporal accuracy. Time advancement is performed
Fig. 1. IPPE 3D with water using 3.5 million nodes; volume fraction of water. Also marked are boundaries and a red arrow indicates the position of future deuterium bombardment location. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Comparison of velocity profiles for different cases at the center of the curved section. Top: velocity profiles for the fluid flow. Bottom: velocity profiles near the wall.
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Fig. 3. Turbulent kinetic energies (TKE) for different models.
Boundary conditions for the flow are (see Fig. 1): (a) velocity inlet at the nozzle; (b) outflow boundary conditions, where required values on the boundary are extrapolated from the interior, at the exit; (c) walls with no slip condition for velocity. Since the nozzle has a contraction ratio of about 10, 1.6 m/s and 2.0 m/s were set as inlet velocities to get bulk velocities of 16 m/s and 20 m/s respectively. 3. Simulation results The IPPE test case consists of two stage SHIMA nozzle, followed by a straight section of 90 mm, followed by curved section of radius 250 mm and an angular span of 36◦ (where the deuterium beams hit the surface, red arrow in Fig. 1), and a width of 70 mm. Note the direction of gravity in Fig. 1. A quadrilateral mesh was used for the whole domain except near the slant corner just on the right of the nozzle in Fig. 1. A fine mesh (x∼10−6 m was used; value recommended by Fluent based on y + ∼1 is x∼10−5 ) was used near the wall for boundary layer resolution and near the interface for resolution of the free surface. Such a fine resolution is required for the LES simulations. For RANS simulations, a coarser mesh could have been used given FLUENT’s enhanced wall treatment option, but for the sake of comparison, identical meshes were used in all cases. For the 3D run, comparisons with 2D cases are made by extracting data at the middle plane. Fig. 1 shows the computed volume fraction diagram for water on IPPE geometry. The interface is the region where blue (air) and red (water) meet. The interface is very smooth, as was also observed in the experiments described in [4]. We note a thickening of the jet as it flows over the curvature, as also shown in later plots in Fig. 1. Fig. 2 compares the velocity magnitude across the liquid (black line at position C in Fig. 1) for the different cases. The bottom figure zooms in near the wall. Note that the cases include 2D and 3D simulations using various turbulence models listed in Table 1 with abbreviation used for them. Also note that the velocity curves are for liquid only and end at the liquid surface (set at volume fraction of 0.5). The green line ending alone is the surface location for LES Smagorinsky model. The set of orange and red lines with different symbols predicting the largest depths are for RANS models while the smallest depth is observed for the LES and laminar runs. As seen in the top figure, all RANS models predict similar velocity profiles (SST, RSM, RKE grouped together in red–orange lines) and thicker boundary layers. The LES WALE model together with the
Fig. 4. Top pressure [in Pascal] contours on the back plate. Bottom: iso-surface for velocity magnitude 14 m/s.
laminar case (red–blue lines) predicts the thinnest boundary layers and a much sharper change toward the bulk velocity. The 3D LES simulation is represented by the solid red line predicting about the same boundary layer thickness as the LES WALE model (dashed red line). However, as seen in the near wall region (bottom, Fig. 2), all LES models have same the velocity gradient as do the RANS models. The LES Smagorinsky and the 3D simulations deviate from the common profile for laminar and LES WALE simulations. Since 3D simulations were also done with LES WALE, the difference is due to three dimensional effects. Also note that simulations for Li flow
A. Prakash et al. / Fusion Engineering and Design 88 (2013) 800–803
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structures near the boundary layer and possibly perturbations in the free surface; on the other hand, the high pressure zone will suppress turbulence helping to stabilize the free surface. Fig. 4 shows pressure contours (top) and iso-surface for a velocity of 14 m/s (bottom) at the back surface of the channel. The velocity of 14 m/s is just at the edge of the boundary layer (see Fig. 2). The straight section has a very smooth profile; however as the flow enters the curved section pressure quickly rises and long streak lines emerge in the velocity iso-surface just after that location. Similar structures in nozzle region were earlier reported by Gordeev et al. [1]. For the current case, these features near the boundary layer do not affect the free surface. Though the 3D simulations are performed with the LES WALE model, the pressure increase is captured equally well by all models in 2D simulations. However a 3D simulation with other RANS models is needed to make sure that the long structures in velocity iso-levels are captured equally well by the RANS models. The perturbations in the free surface levels are well within the acceptable limits of the design (within 1 mm for IFMIF). Fig. 5 shows profiles for free surface levels at locations A, B and C (see Fig. 1) (top figure) and velocity profiles at the free surface at these locations (bottom figure). Free surface levels are smooth but as the flow reaches the middle of curved section, the thickness of the jet increases by about 1 mm. This thickening of the jet is consistent with experimental findings [4]. Another feature to be noted is that on the curved section, the side walls are much more wetted (about 4 mm) than in the straight section (1–2 mm). Velocity profiles are also not as smooth; however the variations are within a magnitude of 2 m/s. Note that the velocities are at the free surface defined as volume fraction of 0.5. 4. Conclusion
Fig. 5. Top: free surface levels. Bottom: fluid velocities at the free surface for locations A, B and C.
using RSM model fall exactly on top of RSM simulations for water. Simulation for a bulk velocity of 20 m/s using RSM stands out having larger gradient at the surface, marginally large boundary layer and about the same free surface level. The dip in velocities near the surface is due to shear induced by low speed air above the Li jet. Fig. 3 compares predictions of Turbulent Kinetic Energies (TKE) for k–ε, RSM and SST models with previous simulations presented in [4] at the center of the curved section. Also shown in the diagram are predictions from a simulation with Li using RSM and with a bulk velocity of 20 m/s again with RSM. All the models predict similar profiles: the TKE is largest at the walls and decays quickly away from the wall; it is then negligible for most of the bulk of the fluid, again increasing at the surface. Note that like in the velocity plots, these plots have been shown only for the fluid (volume fraction 0.5). At the surface, RKE and RSM models predict a much higher value than SST simulation which is very close to the results shown in [4]. Although Loginov et al. used k–ε for their simulations too, they used a much coarser mesh. The prediction for the simulation with a bulk velocity 20 m/s are about 1.5 time larger than for the case with 16 m/s, although the pattern of variation is the same. Curvature can have a double effect on turbulence: on one hand, it can create Görtler vortices which can cause unwanted
Numerical simulations were done for the IPPE geometry using different turbulence models available in the Fluent commercial software. All the models predicted a stable profile for the free surface well within the required limits. However, different models predicted different velocity profiles across the liquid jet and different jet thickness. Predictions of all RANS models were similar and all LES models were similar to each other. Although, the prediction of jet thickness by different models is within 0.5 mm variation which adheres strictly to the design limits of 1 mm for IFMIF. There were some 3D effects noticeable for the velocity profiles but the predicted jet thickness was the same as that for 2D LES models. Values of turbulent kinetic energies predicted by different models were found to be close to each other, particularly in the bulk flow region where maximum heating is supposed to occur. Overall, if the free surface is expected to have eddies and other transient features, LES should be preferred; otherwise RANS models predicted similar steady state flow. 3D simulations performed with LES predicted very interesting features and should be investigated using other models and geometric variations. Among these are variation of the curved section and the affect of bulk velocity on various parameters. References [1] S. Gordeev, V. Heinzel, R. Stieglitz, Hydraulic numerical analyses of the IFMIF target performance, Fusion Engineering and Design 86 (2011) 2545–2584. [2] S. Gordeev, V. Heinzel, D. Leichtle, A. Moeslang, Numerical analysis of free surface instabilities in the IFMIF lithium target, Fusion Engineering and Design 83 (2008) 1524–1528. [3] M. Ida, H. Kondo, K. Nakamura, W. Eiichi, Hydraulic analysis on effects of backplate deformation upon stability of high-speed free-surface lithium flow for IFMIF target design, Fusion Engineering and Design 86 (2011) 2478–2481. [4] N. Loginov, The thermal–hydraulic and technological investigations for validation of the project of lithium circulation loop and neutron lithium target for IFMIF, Obninsk, 2006.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical simulations of the IPPE target geometry flows Akshay Prakash a,∗ , Sotiris Kakarantzas b , Davide Bernardi c , Gioacchino Micciche c , Vincent Massaut d , Bernard Knaepen a a
University Libre de Bruxelles, Belgium University of Thessaly, Volos, Greece EURATOM-ENEA, Brasimore, Italy d SCK-CEN, Mol, Belgium b c
h i g h l i g h t s
We performed numerical simulation of flow over IPPE geometry using turbulence models in FLUENT. Stable free surface profile well within the required design limits was predicted by the models. Velocity profiles across the liquid jet and jet thickness different for different models. There were some 3D effects noticeable for the velocity profiles but the predicted jet thickness similar to 2D models. TKE predicted by different models close to each other and compare will with published data.
a r t i c l e
i n f o
Article history: Received 14 September 2012 Received in revised form 28 January 2013 Accepted 18 February 2013 Available online 11 April 2013 Keywords: IFMIF IPPE Li flow Turbulence Free-surface Curved surface flows
a b s t r a c t A high speed water and liquid lithium (Li) flow is computed over the IPPE geometry to evaluate the performance of different turbulence models in 2D and 3D simulations. Results reported are the thickness of the liquid jet, irregularities in the surface, transient phenomena at the wall which can affect fluid surface and effect of the variation in bulk velocity on these quantities. All models show good near wall resolution of the boundary layer and expected profiles for the free surface flow. Predicted turbulent kinetic energy compare well with published data. Fluctuations of the flow surface at the control location (center of the curved section) and elsewhere are well within 1 mm for all models. However it was observed that the predictions are strongly dependent on the model used. Overall, the predictions of RANS models are close to each other whereas predictions of laminar simulations are close to those obtained with LES models. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The purpose of the International Fusion Materials Irradiation Facility (IFMIF) is to test and qualify materials that can be operated at high temperatures and under intense (neutron) radiation, conditions typical of nuclear fusion devices. In IFMIF, the material samples will be exposed to an intense neutron flux created by bombarding a free surface liquid lithium flow by a dual deuteron beam. A high speed liquid lithium (Li) flow is required to rapidly and continuously evacuate the heat deposited by the two deuterium beams. To test the conceptual design of IFMIF various mock up experiments and simulations on geometries similar to IFMIF were performed. In particular, Gordeev et al. [1,2] studied the effect of unsteady
∗ Corresponding author. Tel.: +32 488134295. E-mail addresses: [email protected], akshay [email protected] (A. Prakash). 0920-3796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.02.106
structures generated by nozzle and straighteners on the free surface and suggested the use of entirely curved backsurface for the facility. Ida et al. [3] have focused on evaluating performance of IFMIF in case of backplate deformation. IPPE (Institute for Physics and Power Engineering) test case [4] is a similar setup where effect of geometrical design and inflow parameters were tested for their effects on the surface stability of the flow. Water was used as the liquid medium. The focus of this paper is on the numerical simulation of water and Li flow for the IPPE geometry. In order to perform high fidelity simulations efficiently, an understanding of various turbulence models on their suitability to reproduce the crucial parameters of the flow discussed below, is required. In order to assess this question, we perform CFD simulations in the turbulent regime where instabilities occurring at the surface of the flow and on the backplate can lead to strong fluctuations of the flow surface. Given the high level of turbulence, several modeling strategies are adopted. First, we use standard RANS modeling and compare the predictions of different models like k–ε, SST and RSM
A. Prakash et al. / Fusion Engineering and Design 88 (2013) 800–803 Table 1 Turbulence models used with their abbreviations. Model
Abbr.
Laminar Navier Stokes Realizable k–ε Shear Stress model Reynolds Stress model Large Eddy Simulation-Smagorinsky subgrid model Large Eddy Simulation-WALE subgrid model Large Eddy Simulations-kinetic energy transport subgrid model 3D LES WALE
Laminar RKE SST RSM LES smag LES wale LES ket 3D
(see Table 1). We also perform some more detailed large-eddy simulations in which the transient properties of large-scale eddies are completely captured while the small-scale turbulence is taken into account through the Smagorinsky or WALE models. A combination of the volume of fluid and level set approaches was used for 2D simulations while for 3D simulations only the volume of fluid method is considered to model the free surface of liquid. Simulations are done with Fluent using default parameters for the turbulence models. The results presented contain velocity profiles on the backplate, the surface structures, the turbulence kinetic energies and the thickness of the flow at different downstream locations. As a parametric analysis of the influence of the average bulk velocity on these flow quantities, simulations were done for bulk velocity of 16 m/s (except for one case where the bulk velocity is 20 m/s).
801
through the SIMPLE scheme. Various turbulence models available in Fluent were used to simulate turbulence: realizable k–ε, Shear Stress Transport (SST), Reynold’s Stress and LES models. k–ε is good for high Reynolds number flows and should predict results with good accuracy away from the wall. SST model combines the k–ε model for flow away from the wall and k–ω model for near wall computations using a blending function. Reynolds Stress model is supposedly the most accurate of the RANS models, solving each of the Reynolds stresses separately (in all 5 additional equations in addition to N–S compared to 2 additional equations for k–ε and k–ω models). LES models are the most computationally intensive models and in theory capture unsteady eddies that can cause perturbations on the free surface. However, they need a fine grid for good resolution. The Smagorinsky subgrid model is known to perform well away from the wall while the WALE model has a better wall behavior. The reader should note that these observations are based on ideas generally accepted in the CFD community and mentioned explicitly in ANSYS Fluent’s manual.
2. Simulation models and boundary conditions The Navier Stokes (N–S) equations are solved using second order spatial and temporal accuracy. Time advancement is performed
Fig. 1. IPPE 3D with water using 3.5 million nodes; volume fraction of water. Also marked are boundaries and a red arrow indicates the position of future deuterium bombardment location. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Comparison of velocity profiles for different cases at the center of the curved section. Top: velocity profiles for the fluid flow. Bottom: velocity profiles near the wall.
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Fig. 3. Turbulent kinetic energies (TKE) for different models.
Boundary conditions for the flow are (see Fig. 1): (a) velocity inlet at the nozzle; (b) outflow boundary conditions, where required values on the boundary are extrapolated from the interior, at the exit; (c) walls with no slip condition for velocity. Since the nozzle has a contraction ratio of about 10, 1.6 m/s and 2.0 m/s were set as inlet velocities to get bulk velocities of 16 m/s and 20 m/s respectively. 3. Simulation results The IPPE test case consists of two stage SHIMA nozzle, followed by a straight section of 90 mm, followed by curved section of radius 250 mm and an angular span of 36◦ (where the deuterium beams hit the surface, red arrow in Fig. 1), and a width of 70 mm. Note the direction of gravity in Fig. 1. A quadrilateral mesh was used for the whole domain except near the slant corner just on the right of the nozzle in Fig. 1. A fine mesh (x∼10−6 m was used; value recommended by Fluent based on y + ∼1 is x∼10−5 ) was used near the wall for boundary layer resolution and near the interface for resolution of the free surface. Such a fine resolution is required for the LES simulations. For RANS simulations, a coarser mesh could have been used given FLUENT’s enhanced wall treatment option, but for the sake of comparison, identical meshes were used in all cases. For the 3D run, comparisons with 2D cases are made by extracting data at the middle plane. Fig. 1 shows the computed volume fraction diagram for water on IPPE geometry. The interface is the region where blue (air) and red (water) meet. The interface is very smooth, as was also observed in the experiments described in [4]. We note a thickening of the jet as it flows over the curvature, as also shown in later plots in Fig. 1. Fig. 2 compares the velocity magnitude across the liquid (black line at position C in Fig. 1) for the different cases. The bottom figure zooms in near the wall. Note that the cases include 2D and 3D simulations using various turbulence models listed in Table 1 with abbreviation used for them. Also note that the velocity curves are for liquid only and end at the liquid surface (set at volume fraction of 0.5). The green line ending alone is the surface location for LES Smagorinsky model. The set of orange and red lines with different symbols predicting the largest depths are for RANS models while the smallest depth is observed for the LES and laminar runs. As seen in the top figure, all RANS models predict similar velocity profiles (SST, RSM, RKE grouped together in red–orange lines) and thicker boundary layers. The LES WALE model together with the
Fig. 4. Top pressure [in Pascal] contours on the back plate. Bottom: iso-surface for velocity magnitude 14 m/s.
laminar case (red–blue lines) predicts the thinnest boundary layers and a much sharper change toward the bulk velocity. The 3D LES simulation is represented by the solid red line predicting about the same boundary layer thickness as the LES WALE model (dashed red line). However, as seen in the near wall region (bottom, Fig. 2), all LES models have same the velocity gradient as do the RANS models. The LES Smagorinsky and the 3D simulations deviate from the common profile for laminar and LES WALE simulations. Since 3D simulations were also done with LES WALE, the difference is due to three dimensional effects. Also note that simulations for Li flow
A. Prakash et al. / Fusion Engineering and Design 88 (2013) 800–803
803
structures near the boundary layer and possibly perturbations in the free surface; on the other hand, the high pressure zone will suppress turbulence helping to stabilize the free surface. Fig. 4 shows pressure contours (top) and iso-surface for a velocity of 14 m/s (bottom) at the back surface of the channel. The velocity of 14 m/s is just at the edge of the boundary layer (see Fig. 2). The straight section has a very smooth profile; however as the flow enters the curved section pressure quickly rises and long streak lines emerge in the velocity iso-surface just after that location. Similar structures in nozzle region were earlier reported by Gordeev et al. [1]. For the current case, these features near the boundary layer do not affect the free surface. Though the 3D simulations are performed with the LES WALE model, the pressure increase is captured equally well by all models in 2D simulations. However a 3D simulation with other RANS models is needed to make sure that the long structures in velocity iso-levels are captured equally well by the RANS models. The perturbations in the free surface levels are well within the acceptable limits of the design (within 1 mm for IFMIF). Fig. 5 shows profiles for free surface levels at locations A, B and C (see Fig. 1) (top figure) and velocity profiles at the free surface at these locations (bottom figure). Free surface levels are smooth but as the flow reaches the middle of curved section, the thickness of the jet increases by about 1 mm. This thickening of the jet is consistent with experimental findings [4]. Another feature to be noted is that on the curved section, the side walls are much more wetted (about 4 mm) than in the straight section (1–2 mm). Velocity profiles are also not as smooth; however the variations are within a magnitude of 2 m/s. Note that the velocities are at the free surface defined as volume fraction of 0.5. 4. Conclusion
Fig. 5. Top: free surface levels. Bottom: fluid velocities at the free surface for locations A, B and C.
using RSM model fall exactly on top of RSM simulations for water. Simulation for a bulk velocity of 20 m/s using RSM stands out having larger gradient at the surface, marginally large boundary layer and about the same free surface level. The dip in velocities near the surface is due to shear induced by low speed air above the Li jet. Fig. 3 compares predictions of Turbulent Kinetic Energies (TKE) for k–ε, RSM and SST models with previous simulations presented in [4] at the center of the curved section. Also shown in the diagram are predictions from a simulation with Li using RSM and with a bulk velocity of 20 m/s again with RSM. All the models predict similar profiles: the TKE is largest at the walls and decays quickly away from the wall; it is then negligible for most of the bulk of the fluid, again increasing at the surface. Note that like in the velocity plots, these plots have been shown only for the fluid (volume fraction 0.5). At the surface, RKE and RSM models predict a much higher value than SST simulation which is very close to the results shown in [4]. Although Loginov et al. used k–ε for their simulations too, they used a much coarser mesh. The prediction for the simulation with a bulk velocity 20 m/s are about 1.5 time larger than for the case with 16 m/s, although the pattern of variation is the same. Curvature can have a double effect on turbulence: on one hand, it can create Görtler vortices which can cause unwanted
Numerical simulations were done for the IPPE geometry using different turbulence models available in the Fluent commercial software. All the models predicted a stable profile for the free surface well within the required limits. However, different models predicted different velocity profiles across the liquid jet and different jet thickness. Predictions of all RANS models were similar and all LES models were similar to each other. Although, the prediction of jet thickness by different models is within 0.5 mm variation which adheres strictly to the design limits of 1 mm for IFMIF. There were some 3D effects noticeable for the velocity profiles but the predicted jet thickness was the same as that for 2D LES models. Values of turbulent kinetic energies predicted by different models were found to be close to each other, particularly in the bulk flow region where maximum heating is supposed to occur. Overall, if the free surface is expected to have eddies and other transient features, LES should be preferred; otherwise RANS models predicted similar steady state flow. 3D simulations performed with LES predicted very interesting features and should be investigated using other models and geometric variations. Among these are variation of the curved section and the affect of bulk velocity on various parameters. References [1] S. Gordeev, V. Heinzel, R. Stieglitz, Hydraulic numerical analyses of the IFMIF target performance, Fusion Engineering and Design 86 (2011) 2545–2584. [2] S. Gordeev, V. Heinzel, D. Leichtle, A. Moeslang, Numerical analysis of free surface instabilities in the IFMIF lithium target, Fusion Engineering and Design 83 (2008) 1524–1528. [3] M. Ida, H. Kondo, K. Nakamura, W. Eiichi, Hydraulic analysis on effects of backplate deformation upon stability of high-speed free-surface lithium flow for IFMIF target design, Fusion Engineering and Design 86 (2011) 2478–2481. [4] N. Loginov, The thermal–hydraulic and technological investigations for validation of the project of lithium circulation loop and neutron lithium target for IFMIF, Obninsk, 2006.