Dr. J. Wolters. FZJ-ZAT-379 January Forschungszentrum Jülich GmbH, FZJ

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1 Forschungszentrum Jülich GmbH, FZJ ZAT-Report FZJ-ZAT-379 January 2003 Benchmark Activity on Natural Convection Heat Transfer Enhancement in Mercury with Gas Injection authors Dr. J. Wolters abstract A natural heat transfer experiment in mercury with gas injection is described in [1]. A vertical enclosure heated on one face at constant heat flux and cooled on the opposite face was used for the experiment. Local heat transfer and void fraction measurements were made with thermocouple and double-conductivity probes and the heat transfer enhancement by the gas bubbles was investigated. This experiment on natural convection heat transfer enhancement in mercury with gas injection was chosen by the Benchmark Working Group as a benchmark within the ASCHLIM project to assess the reliability of CFD codes with respect to Heavy Liquid Metal flows (HLM-flows). A series of numerical simulations were performed with the CFD code Fluent in order to investigate the agreement with the experimental results. Conclusive results were achieved for the natural convection case without bubble injection. Significant deviations occur regarding the bubble trajectories if bubble injection is considered.

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3 ZAT-Report No. 379, Rev. 0, January 2003 Page 3 of 54 Contents Page Contents Introduction Description of the experiment CFD calculations Computational mesh Boundary conditions Physical properties of mercury and nitrogen Viscous models Results Without gas injection Effect of side walls Effect of thermally stratified bulk fluid Effect of viscous model Effect of heat flux With gas injection Bubble trajectories for case W10, Q Effect of heat flux Effect of side walls Summary & Conclusions Literature List of Figures List of Tables... 54

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5 ZAT-Report No. 379, Rev. 0, January 2003 Page 5 of Introduction A natural heat transfer experiment in mercury with gas injection is described in [1]. A vertical enclosure heated on one face at constant heat flux and cooled on the opposite face was used for the experiment. Local heat transfer and void fraction measurements were made with thermocouple and double-conductivity probes and the heat transfer enhancement by the gas bubbles was investigated. The experiment on natural convection heat transfer enhancement in mercury with gas injections was chosen by the Benchmark Working Group as a benchmark within the ASCHLIM project to assess the reliability of CFD codes with respect to Heavy Liquid Metal flows (HLM-flows). 2. Description of the experiment The experimental set-up for the experiments on natural convection heat transfer enhancement in mercury with gas injection is schematically shown in Figure 1. A detailed description of the experimental set-up is given in [1].

6 ZAT-Report No. 379, Rev. 0, January 2003 Page 6 of 54 Figure 1: Experimental set-up The height of the cell is 40.0 cm, the depth is 20.3 cm and the cell is 7.0 cm in width. A heated vertical plate is used to apply a constant heat flux of up to 16 kw/m² on the left side of the mercury cell. The opposite side of the cell is water cooled. Inside the cell a row of eleven evenly-spaced gas injection tubes was installed 2 mm away from the heated wall and at the same height than the leading edge (cp. Figure 2). Nitrogen gas was used in all experiments with gas injection.

7 ZAT-Report No. 379, Rev. 0, January 2003 Page 7 of 54 Figure 2: Perspective view of experimental set-up with gas injection tubes In the experiments the heat flux was adjusted by the voltage and current of each heater. The water flow-rate of the cooling side was adjusted in such a way that the bulk temperature at the midpoint (midpoint along the X and Y axes) maintains approximately at 20 C. 3. CFD calculations For the calculations performed at FZJ the CFD code FLUENT [2] (release 6.0) was used. A detailed description of the calculations is given in the following Computational mesh A two-dimensional model was mainly used for the calculations, neglecting three-dimensional effects due to the side walls. Based on a study of Mallinson and de Vahl Davis [3] the threedimensional effects were assessed for the experimental set-up in [1]. In the experiment the three-dimensional effects will to some extent influence the results for the central X-Y plane and compared to the results for the central plane in the enclosure, the two-dimensional calculations will slightly overpredict the Nusselt number for the single-phase flow. Moreover

8 ZAT-Report No. 379, Rev. 0, January 2003 Page 8 of 54 the effect of the side walls was investigated in separate calculations for the single-phase and two-phase flow, that are described in chapter and The CFD model is shown in Figure 3. The free surface is not explicitly modeled but is considered by a wall with no wall shear stress (frictionless slip) or just by a symmetry boundary condition. The negligible effect of grid size was checked by additional calculations with a refined and coarsened mesh. boundaries mesh heated wall slipping wall cooled wall position of bubble injection x Figure 3: CFD model 3.2. Boundary conditions A constant heat flux according to the load case (cp. Table 1) is applied to the heated left wall of the cell. At the water-cooled right wall a convection boundary condition with a constant free-stream temperature T 4 of 10 C is considered. The heat transfer coefficient was adjusted during the calculations to get a mid-point temperature of about 20 C. For all solid walls a noslip boundary condition is considered while for the free-surface a wall with no wall shear stress or just a symmetry boundary condition is used.

9 ZAT-Report No. 379, Rev. 0, January 2003 Page 9 of 54 load case heat flux, heated side [W/m²] heat-transfer coefficient, cooled side [W/m² K] W W W W W Table 1: Energy boundary conditions For the nitrogen bubbles the Lagrangian Discrete Phase Model in Fluent is used. In this model the bubble acceleration is calculated by the drag force, the gravity force, the pressure gradient force and the virtual mass force. A lift force due to shear was not considered in the calculations. In Fluent the lift force (Saffman lift force) is intended for small particle Reynolds numbers. Also, the particle Reynolds number based on the particle-fluid velocity difference must be smaller than the square root of the particle Reynolds number based on the shear field. Since this restriction is valid for submicron particles, it is recommended by Fluent to use this option only for submicron particles [2]. Therefore the lift force in Fluent can not be used for the gas bubbles in this case. The interaction of the bubbles with the continuous phase is considered, but the direct effect of the bubbles on the generation or dissipation of turbulence in the continuous phase is not covered by the model. For the drag law it was assumed that all bubbles are spherical. The dispersion of the bubbles due to turbulence is considered. Stochastic tracking is used with the discrete random walk model implemented in Fluent. The position of the bubble release is two millimeters away from the heated wall and at the same height than the leading edge (cp. Figure 3). According to Figure 16 of [1] the diameter of the bubbles is set to 1.25 mm for the cases with a total gas injection of 4.3 cm³/sec. These cases are labeled with Q43, while the cases without gas injection are labeled with Q0. In the two-dimensional model the gas injection rate is related to a depth of 1 m. So a mass flow-rate of

10 ZAT-Report No. 379, Rev. 0, January 2003 Page 10 of 54 m& N2 = Q N2 ρ d N2 = 4.3 cm³ / s m 6 kg / cm³ = kg s m is set up for these calculations with gas injection Physical properties of mercury and nitrogen For the calculation, temperature dependent properties for mercury were used. Because the temperature range inside the mercury is quite small for the given boundary conditions, a linear variation between 0 C and 50 C is used for all properties. The corresponding values were derived from [4] and are listed below. Temperature Property Units t = 0 C t = 50 C Density ρ kg / m³ Thermal conductivity λ W / (m K) Molecular viscosity µ kg / (m s) specific heat at constant pressure c p J / (kg K) Table 2: Physical properties of mercury For the nitrogen bubbles the following constant properties were used for the calculation: density: kg/m³ thermal conductivity: W/(m K) heat capacity: J/(kg K) 3.4. Viscous models The calculations were mainly done using the RNG k-ε turbulence model. The RNG-based k-ε model is derived from the instantaneous Navier-Stokes equations, using a mathematical technique called renormalization group (RNG) methods. The analytical derivation results in a model with constants different from those in the standard k-ε model, and additional terms

11 ZAT-Report No. 379, Rev. 0, January 2003 Page 11 of 54 and functions in the transport equations for k and ε [2]. It also has a turbulent viscosity expression ( Differential Viscosity Model ) as an option, which is valid across the full range of flow conditions, from low to high Reynolds numbers. This viscosity model was enabled for all calculations. A more comprehensive description of RNG theory and its application to turbulence can be found in [5]. A two-layer zonal model was used for the near-wall treatment. For the cases W4 and W10 additional calculations were done with the laminar model for comparison reasons. 4. Results The main aspect of the experiments was the determination of the convection heat transfer in mercury. In [1], [6] and [7] the experimental heat transfer results are mainly presented in the form Nu x (Bo * x) (local Nusselt number as a function of the local modified Boussinesq number). The definition of the local Nusselt number and the local modified Boussinesq number is given below. Nu x = λ q' & ' x ( T T ) w bulk Bo 4 2 q' ' x g β c * p x 3 = & λ 2 ρ with x: position along the heated wall q& ' ' : heat flux for the heated wall T w : wall temperature T bulk : local bulk temperature (temperature at a certain distance to the wall, where the temperature profile for a path perpendicular to the wall gets horizontal) g: gravity constant (9.81 m/s²) β: coefficient of volumetric thermal expansion (170 1/K for given temperature dependant mercury density)

12 ZAT-Report No. 379, Rev. 0, January 2003 Page 12 of Without gas injection Effect of side walls In a first set of calculations for the laminar case W4Q0 the effect of the limited width of the mercury enclosure was investigated. Of course the effect of side walls gets more important for higher heat flux conditions and in the presence of gas bubbles, but this first set of calculations was done to show, that the effect of side walls is not responsible for the deviation of the calculated Nusselt number in the laminar regime from the laminar correlation. The results for the two-dimensional calculation was compared to the results for a threedimensional half-model of the enclosure. In both cases a laminar viscous model was used for the calculation. In Figure 4 the velocity distribution is shown for the three-dimensional calculation in comparison to the two-dimensional calculation and in Figure 5 the comparison is shown for the temperature distribution. The effect of the side walls on the velocity and temperature distribution in the central vertical plane is negligible for the given arrangement. Figure 4: Velocity distribution for the three- and two-dimensional model for load case W4Q0 (laminar viscous model)

13 ZAT-Report No. 379, Rev. 0, January 2003 Page 13 of 54 Figure 5: Temperature distribution for the three- and two-dimensional model for load case W4Q0 (laminar viscous model) In Figure 6 the calculated and measured Nusselt numbers are shown as a function of the modified Boussinesq number in comparison to the laminar correlation Nu x 1 * 2 ( Gr Pr ) 5 = 0.732, x that is given in [8] for an unstratified bulk fluid. Between the two- and three-dimensional calculation there is no significant deviation. But it is obvious that the calculated Nusselt numbers are much higher than the laminar correlation and the measured Nusselt numbers. The reason for this phenomena is probably a thermally stratified bulk fluid. This will be discussed in detail in the next chapter.

14 ZAT-Report No. 379, Rev. 0, January 2003 Page 14 of W4, Q0, laminar W4, Q0, laminar (3d) W4, Q0, experiment laminar correlation Nu x E3 1E4 1E5 Bo x * 1E6 1E7 1E8 Figure 6: Local Nusselt numbers as a function of the modified local Boussinesq number for load case W4Q0 The results for the maximum heat flux boundary condition of W/m² are shown in Figure 7 (velocity distribution) and Figure 8 (temperature distribution). For these calculations the RNG k-ε model was used. Again, the velocity and temperature distributions agree very well for the central plane and there is no significant deviation in the calculated local Nusselt number (cp. Figure 9).

15 ZAT-Report No. 379, Rev. 0, January 2003 Page 15 of 54 Figure 7: Velocity distribution for the three- and two-dimensional model for load case W160Q0 (RNG k-ε model) Figure 8: Temperature distribution for the three- and two-dimensional model for load case W160Q0 (RNG k-ε model)

16 ZAT-Report No. 379, Rev. 0, January 2003 Page 16 of W160, Q0, RNG k-eps W160, Q0, RNG k-eps (3d) Nu x E5 1E6 1E7 Bo x * 1E8 1E9 1E10 Figure 9: Local Nusselt numbers as a function of the modified local Boussinesq number for load case W160Q Effect of thermally stratified bulk fluid A thermally stratified bulk fluid can have a significant effect on the local Nusselt number. In [8] this effect was studied in detail for stratification parameters up to 0.1. The stratification parameter S is defined by a S = λ q' & ', where a is the bulk temperature gradient. It was found that the enhancement of Nu x with stratification can reach a factor of 3 or 4 for S approaching 0.1. The reason for this effect is the increase of heat transfer rate due to the reduction of boundary layer thickness caused by the thermal stratification. In our cases for low heat fluxes the stratification factor will even exceed 0.1 (cp. Figure 10), so that a significant enhancement of the local Nusselt number can be expected for the given arrangement.

17 ZAT-Report No. 379, Rev. 0, January 2003 Page 17 of 54 1,5 1 0,5 T bulk, K 0-0,5 0 0,05 0,1 0,15 0,2 0,25 0,3 0, ,5 Q0: S=0.147 vertical distance to leading edge, m Figure 10: Bulk temperature (difference to the mid-point temperature) as a function of the vertical distance to the leading edge for load case W4Q0 In order to proof that the deviation does not occur due to a bad prediction of the CFD code, an additional calculation was performed for an arrangement comparable to that described in [8]. For the calculation a heat flux of 370 W/m² was used for the heated vertical plate on the left side of the model (cp. Figure 11). To avoid any effect of a thermally stratified bulk fluid, a transient calculation was performed with an initial homogeneous temperature of 293 K. The postprocessing was done for the conditions that were reached after 180 seconds and 3600 seconds. In Figure 11 and Figure 12 the temperature and velocity distribution after 180 seconds can be seen. The bulk temperature is still at the initial temperature of 293 K ( T = 0 K) and therefore the stratification parameter S is 0 for this case (cp Figure 13). In Figure 14 the local Nussel number is plotted for this case as a function of the local modified Boussinesq number and a good agreement with the laminar correlation is achieved. An additional calculation with a heat flux of W/m² (like in [8]) also agrees very well with the laminar correlation (cp. Figure 14) if the bulk fluid is thermally unstratified. In Figure 15 and Figure 16 the velocity and temperature distribution is shown for t = 3600 s. As can be seen from Figure 16 and Figure 13, the bulk fluid is partly stratified. In conformity with the investigations in [8] the local Nusselt number increases compared to the unstratified bulk fluid.

18 ZAT-Report No. 379, Rev. 0, January 2003 Page 18 of 54 This may partly explain the deviation between the calculation and the laminar correlation shown in Figure 6 for a low heat flux but a high stratification parameter of In addition to this, deviations may occur due to the flow conditions at the bottom and the top of the heated plate, caused by the limited height of the enclosure. Heated wall Figure 11: Velocity distribution for the test arrangement according to [8] after 180 s (heat flux: 370 W/m², laminar viscous model).

19 ZAT-Report No. 379, Rev. 0, January 2003 Page 19 of 54 Figure 12: Temperature distribution for the test arrangement according to [8] after 180 s (heat flux: 370 W/m², laminar viscous model). 293,7 293,6 bulk temperature, K 293,5 293,4 293,3 293,2 293,1 S = S = S = t = 180 s t = 3600 s ,9 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 vertical distance to the leading edge, m Figure 13: Bulk temperature as a function of the vertical distance to the leading edge for the test arrangement according to [8]

20 ZAT-Report No. 379, Rev. 0, January 2003 Page 20 of unstratified bulk fluid, q''=370 W/m² partly stratified bulk fluid, q''=370 W/m² laminar correlation unstratified bulk fluid, q''=18000 W/m² Nu x E3 1E4 1E5 1E6 1E7 1E8 1E9 1E10 Bo x * Figure 14: Local Nusselt number as a function of the modified local Boussinesq number for the test arrangement according to [8] Figure 15: Velocity distribution for the test arrangement according to [8] after 3600 s (heat flux: 370 W/m², laminar viscous model).

21 ZAT-Report No. 379, Rev. 0, January 2003 Page 21 of 54 Figure 16: Temperature distribution for the test arrangement according to [8] after 3600 s (heat flux: 370 W/m², laminar viscous model) Effect of viscous model For higher heat fluxes and for the cases with bubble injection turbulence has to be considered in the CFD calculations. The RNG k-ε model is used for those calculations. The suitability of this turbulence model for almost laminar flows was investigated in the following. For the lowest heat fluxes (370 W/m² and 970 W/m²) the results for the RNG k-ε model were compared to those of the laminar model. In Figure 17 the velocity distribution and in Figure 18 the temperature distribution is shown for the RNG k-ε model and the load case W4. The maximum velocity for the RNG k-ε model is smaller than those for the laminar model (cp. Figure 4 and Figure 17), because the effective viscosity is increased due to turbulence for the calculation with the RNG k-ε model. Although this deviation occurs with respect to the velocity distribution, the deviation for the temperature is quite small (cp. Figure 5 and Figure 18).

22 ZAT-Report No. 379, Rev. 0, January 2003 Page 22 of 54 Figure 17: Velocity distribution for the RNG k-ε model (load case W4Q0) Figure 18: Temperature distribution for the RNG k-ε model (load case W4Q0)

23 ZAT-Report No. 379, Rev. 0, January 2003 Page 23 of 54 Regarding the local Nusselt number the effect of the viscous model is negligible compared to the effect of a stratified bulk fluid (cp. Figure 19). Similar results were achieved for the load case W10Q0 with a heat flux of 970 W/m² (cp. Figure 20). 100 W4, Q0, RNG k-eps W4, Q0, laminar Nu x E3 1E4 1E5 Bo x * 1E6 1E7 1E8 Figure 19: Local Nusselt number as a function of the modified local Boussinesq number for the laminar model and the RNG k-ε model (load case W4Q0) 100 W10, Q0, RNG k-eps W10, Q0, laminar Nu x E3 1E4 1E5 1E6 Bo x * 1E7 1E8 1E9 Figure 20: Local Nusselt number as a function of the modified local Boussinesq number for the laminar model and the RNG k-ε model (load case W10Q0)

24 ZAT-Report No. 379, Rev. 0, January 2003 Page 24 of Effect of heat flux In the following chapter the results for all higher heat flux boundary conditions are briefly presented. For those calculations the RNG k-ε model was used. In Figure 21 the calculated Nusselt numbers are shown in comparison to the experimental results. The slope of the calculated correlation agrees quite well with the laminar correlation but compared to the experimental results the shape of the correlations is different. Probably this deviation can be explained by the limited vertical size of the mercury enclosure, that caused some additional effects at the lower and upper end of the heated plate during the experiment. For the upper half of the heated plate we can see from the experimental results as well as from the calculations that the Nusselt number will decrease with increasing heat flux. Possibly the decreasing stratification parameter is one reason for this effect. The bulk temperature distribution and the corresponding stratification parameter S is shown in Figure W40, Q0, calculation W80, Q0, calculation W160, Q0, calculation W40, Q0, experiment W80, Q0, experiment W160, Q0, experiment laminar correlation Nu x E4 1E5 1E6 1E7 1E8 1E9 1E10 Bo x * Figure 21: Local Nusselt number as a function of the modified local Boussinesq number for heat-flux cases W40, W80 and W160 compared to the experimental results

25 ZAT-Report No. 379, Rev. 0, January 2003 Page 25 of W40, Q0 W80, Q0 W160, Q0 Q80: S=0.033 T bulk, K Q40: S= ,05 0,1 0,15 0,2 0,25 0,3 0,35 Q160: S=0.021 vertical distance to leading edge, m Figure 22: Bulk temperature (difference to the mid-point temperature) as a function of the vertical distance to the leading edge Velocity and temperature distributions are shown in Figure 23 and Figure 24 for the case W10Q0, in Figure 25 and Figure 26 for the case W40Q0, in Figure 27 and Figure 28 for case W80Q0 and in Figure 29 and Figure 30 for case W160Q0.

26 ZAT-Report No. 379, Rev. 0, January 2003 Page 26 of 54 Figure 23: Velocity distribution within the cell for load case W10, Q0 Figure 24: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W10, Q0

27 ZAT-Report No. 379, Rev. 0, January 2003 Page 27 of 54 Figure 25: Velocity distribution within the cell for load case W40, Q0 Figure 26: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W40, Q0

28 ZAT-Report No. 379, Rev. 0, January 2003 Page 28 of 54 Figure 27: Velocity distribution within the cell for load case W80, Q0 Figure 28: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W80, Q0

29 ZAT-Report No. 379, Rev. 0, January 2003 Page 29 of 54 Figure 29: Velocity distribution within the cell for load case W160, Q0 Figure 30: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W160, Q0

30 ZAT-Report No. 379, Rev. 0, January 2003 Page 30 of With gas injection Bubble trajectories for case W10, Q43 First of all the bubble motion was investigated for the load case W10Q43. For this case experimental results are available for the bubble velocity and the bubble distribution [1; 6]. In Figure 31 the measured void fraction is shown for a horizontal plane 11 cm above the leading edge. While for the experiment the bubbles were driven away from the heated wall, the bubbles stay close to the wall in the calculation. Apparently the bubble trajectories are strongly influenced by the shear flow near the heated wall in the experiment and this effect it not considered in the calculation. 0,014 0,012 calculation experiment void fraction α 0,010 0,008 0,006 0,004 0,002 0, distance to heated wall, mm Figure 31: Void fraction profiles for a path perpendicular to the heated wall and 11 cm above the leading edge (load case W10Q43) As a matter of course all other results are influenced by the bubble distribution. If the bubble trajectories are not predicted correct in the calculation the velocity distribution will also deviate from the experimental results. In Figure 32 the bubble rise velocity is shown for the same path than in Figure 31. In the experiment the bubble velocity is about 0.2 m/s. Unfortunately there is no data available for the fluid velocity, so that the relative velocity of the bubbles is not known. In Figure 33 the calculated bubble and fluid velocity is shown. The relative velocity of the bubbles, that is equal to the terminal rise velocity in a stagnant fluid, is about 0,2 m/s.

31 ZAT-Report No. 379, Rev. 0, January 2003 Page 31 of 54 bubble velocity v B, m/s 0,30 0,25 0,20 experiment calculation 0, distance to heated wall, mm Figure 32: Bubble velocity profiles for a path perpendicular to the heated wall and 11 cm above the leading edge (load case W10Q43) 0,35 0,30 bubble velocity fluid velocity 0,25 velocity, m/s 0,20 0,15 0,10 0,05 0, distance to heated wall, mm Figure 33: Calculated bubble and fluid velocity profiles for a path perpendicular to the heated wall and 11 cm above the leading edge (load case W10Q43) The enhancement of the local Nusselt number due to the bubbles is shown in Figure 34. While for the experiment the Nusselt number is increased by a factor of 1.4 (upper side of the heated plate) up to 2.5 (lower side of the heated plate), the enhancement of the local

32 ZAT-Report No. 379, Rev. 0, January 2003 Page 32 of 54 Nusselt number is much larger for the calculation (2.1 up to 3.7 in the same region of the heated plate). This is due to the fact that in the calculation most of the bubbles move close to the wall and therefore influence the heat transfer in the boundary layer much stronger than in the experiment W10, Q0, calculation W10, Q43, calculation W10, Q0, experiment W10, Q43, experiment Nu x 100 x 2.1 x E5 1E6 Bo x * 1E7 1E8 Figure 34: Local Nusselt numbers as a function of the modified local Boussinesq number for load case W10, Q0 and Q43 The temperature and velocity profiles are shown in the next chapter Effect of heat flux The main results for all heat flux conditions are shown in the following. The enhancement of the local Nusselt number due to bubble injection is shown in Figure 35, Figure 36, Figure 37, Figure 38 and Figure 39 for the cases W4, W40, W80 and W 160. For the lower and upper side of the plate the enhancement factor is also given in the diagrams. Like in the experiment the enhancement decreases with higher heat fluxes and higher turbulence, respectively. But this effect is much stronger in the experiment than in the calculation. For high heat fluxes there is almost no Nusselt number enhancement due to the gas injection in the experiment. Unfortunately in [1] and [6] only some of the experimental data are provided, so that a detailed comparison is not possible here. The main reason for the deviation is again the bubble motion predicted by the CFD code. While in the experiment for the turbulent regime (W40, W80 and W160) more bubbles are exterior to the boundary layer and therefore do not

33 ZAT-Report No. 379, Rev. 0, January 2003 Page 33 of 54 effect the heat transfer in the boundary layer so much, most of the bubbles will stay close to the wall for the calculation. In addition to this, the effect of the side walls is much stronger for the cases with bubble injection than for the laminar case. This will be discussed in the next chapter for the case W160Q W4, Q0 W4, Q x 2.3 Nu x 10 x E3 1E4 1E5 Bo x * 1E6 1E7 1E8 Figure 35: Local Nusselt number as a function of the modified local Boussinesq number for load case W4 with and without gas injection 1000 W10, Q0 W10, Q Nu x 10 x E3 1E4 1E5 1E6 Bo x * 1E7 1E8 1E9 Figure 36: Local Nusselt number as a function of the modified local Boussinesq number for load case W10 with and without gas injection

34 ZAT-Report No. 379, Rev. 0, January 2003 Page 34 of W40, Q0 W40, Q x 1.7 Nu x 10 x E3 1E4 1E5 1E6 Bo x * 1E7 1E8 1E9 Figure 37: Local Nusselt number as a function of the modified local Boussinesq number for load case W40 with and without gas injection 1000 W80, Q0 100 W80, Q43 x 1.6 Nu x x E4 1E5 1E6 Bo x * 1E7 1E8 1E9 Figure 38: Local Nusselt number as a function of the modified local Boussinesq number for load case W80 with and without gas injection

35 ZAT-Report No. 379, Rev. 0, January 2003 Page 35 of W160, Q0 100 W160, Q43 x 1.4 Nu x x E5 1E6 1E7 Bo x * 1E8 1E9 1E10 Figure 39: Local Nusselt number as a function of the modified local Boussinesq number for load case W160 with and without gas injection The decrease in stratification due to the bubbles is predicted quite well by the CFD code. In Figure 40 the measured bulk temperature for the case W80 is compared with the numerical results. Because only the temperature gradient parallel to the heated wall is of interest, the mid-point temperature in the calculation was adjusted to get the same level than in the experiment.

36 ZAT-Report No. 379, Rev. 0, January 2003 Page 36 of W80-Q0, experiment W80-Q0, calculation* W80-Q0, calculation W80-Q43, calculation* 30 T B [ C] * Niveau of the calculated bulk temperature distribution was adjusted according to the experiment 20 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 x-distance [m] Figure 40: Bulk temperature (difference to the mid-point temperature) as a function of the vertical distance to the leading edge for load case W80 with and without bubble injection The results for the cases W4, W10, W40, W80 and W160 regarding the bulk temperature gradient and stratification parameter S are presented in Figure 41, Figure 42, Figure 43, Figure 44 and Figure 45. Velocity and temperature distributions are shown in Figure 46 and Figure 47 for the case W4Q43, in Figure 48 and Figure 49 for the case W10Q43, in Figure 50 and Figure 51 for the case W40Q43, in Figure 52 and Figure 53 for case W80Q43 and in Figure 54 and Figure 55 for case W160W43.

37 ZAT-Report No. 379, Rev. 0, January 2003 Page 37 of 54 1,5 1 Tbulk, K 0,5 0-0,5 Q43: S= ,05 0,1 0,15 0,2 0,25 0,3 0,35-1 Q0: S= ,5 vertical distance to leading edge, m Figure 41: Bulk temperature as a function of the vertical distance to the leading edge for load case W4 2,5 2 1,5 Tbulk, K 1 0,5 0-0,5-1 -1,5-2 Q43: S= ,05 0,1 0,15 0,2 0,25 0,3 0,35 Q0: S=0.097 vertical distance to leading edge, m Figure 42: Bulk temperature as a function of the vertical distance to the leading edge for load case W10

38 ZAT-Report No. 379, Rev. 0, January 2003 Page 38 of Tbulk, K Q43: S= ,05 0,1 0,15 0,2 0,25 0,3 0,35 Q0: S=0.049 vertical distance to leading edge, m Figure 43: Bulk temperature as a function of the vertical distance to the leading edge for load case W Tbulk, K Q43: S=0, ,05 0,1 0,15 0,2 0,25 0,3 0,35 Q0: S=0,033 vertical distance to leading edge, m Figure 44: Bulk temperature as a function of the vertical distance to the leading edge for load case W80

39 ZAT-Report No. 379, Rev. 0, January 2003 Page 39 of Tbulk, K Q43: S= ,05 0,1 0,15 0,2 0,25 0,3 0,35 Q0: S=0.021 vertical distance to leading edge, m Figure 45: Bulk temperature as a function of the vertical distance to the leading edge for load case W160 Figure 46: Velocity distribution within the cell for load case W4, Q43

40 ZAT-Report No. 379, Rev. 0, January 2003 Page 40 of 54 Figure 47: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W4, Q43 Figure 48: Velocity distribution within the cell for load case W10, Q43

41 ZAT-Report No. 379, Rev. 0, January 2003 Page 41 of 54 Figure 49: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W10, Q43 Figure 50: Velocity distribution within the cell for load case W40, Q43

42 ZAT-Report No. 379, Rev. 0, January 2003 Page 42 of 54 Figure 51: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W40, Q43 Figure 52: Velocity distribution within the cell for load case W80, Q43

43 ZAT-Report No. 379, Rev. 0, January 2003 Page 43 of 54 Figure 53: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W80, Q43 Figure 54: Velocity distribution within the cell for load case W160, Q43

44 ZAT-Report No. 379, Rev. 0, January 2003 Page 44 of 54 Figure 55: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W160, Q Effect of side walls For the Case W160Q43 additional three-dimensional calculations were performed in order to study the effect of the limited width of the enclosure. Moreover the effect of the single gas injection tubes was considered in the three-dimensional calculation, while in the twodimensional calculation it was assumed, that the gas is injected along an uninterrupted line. Steady-state conditions were not achieved for the three-dimensional calculation. The postprocessing was done for a certain point in time in order to show main effects, but the detailed results may be different for another time-step. The velocity distribution for the three-dimensional calculation is shown in Figure 56 in comparison to the two-dimensional result. As can be seen from Figure 56 strong differences occur for this load case. The maximum velocity in the central vertical plane is much higher than in the two-dimensional calculation. Moreover the velocity distribution in the vertical planes significantly changes while moving towards the side-walls. Due to these differences in the velocity distribution, the temperature distribution also differs significantly (cp. Figure 57).

45 ZAT-Report No. 379, Rev. 0, January 2003 Page 45 of 54 Although significant differences for the velocity and temperature distributions could be identified, the differences in the calculated Nusselt numbers are surprisingly small (cp. Figure 58), so that the overestimation of the local Nusselt number enhancement by the CFD calculation can not conclusively be explained by the neglect of three-dimensional effects. Figure 56: Velocity distribution for the three- and two-dimensional model for load case W160Q43 (RNG k-ε model)

46 ZAT-Report No. 379, Rev. 0, January 2003 Page 46 of 54 Figure 57: Temperature distribution for the three- and two-dimensional model for load case W160Q43 (RNG k-ε model) 1000 W160, Q43, RNG k-eps W160, Q43, RNG k-eps (3d) Nu x E5 1E6 1E7 Bo x * 1E8 1E9 1E10 Figure 58: Local Nusselt numbers as a function of the modified local Boussinesq number for load case W160Q43

47 ZAT-Report No. 379, Rev. 0, January 2003 Page 47 of Summary & Conclusions Regarding the benchmark activity on natural convection heat transfer enhancement in mercury with gas injection calculations were performed with the CFD code Fluent. Conclusive results were achieved for the natural convection case without bubble injection. Significant deviations occur regarding the bubble trajectories if bubble injection is considered. The main conclusions are summarized in the following: The effect of the side walls of the enclosure is negligible for the cases without gas bubbles. A stratified bulk fluid will increase the local Nusselt number significantly. For an unstratified bulk fluid the laminar correlation could be reproduced with the CFD code. The results for the RNG k-ε model with respect to the local Nusselt number are quite satisfactory in the laminar regime. For higher heat fluxes the local Nusselt number slightly decreases, probably because the effect of the stratified bulk fluid decreases (decreasing stratification parameter S). The agreement between experimental and numerical results for the single-phase are not yet satisfactory. More detailed information are needed regarding the experimental boundary conditions and results to understand the deviations completely. The bubble motion within the shear flow near the wall is not predicted very well. While in the experiment the bubbles were driven away from the wall, the bubbles stay close to the wall for the calculation. The enhancement of the heat transfer by the gas bubbles is overestimated by the CFD calculation, probably because of the poor agreement of bubble trajectories. The effect of decreasing Nusselt number enhancement with increasing heat flux is much stronger in the experiment than in the calculation. Although significant differences could be identified between the three- and twodimensional calculations if gas injection is considered, the overestimation of the local Nusselt number enhancement by the two-dimensional CFD calculations can not conclusively be explained by the neglect of three-dimensional effects.

48 ZAT-Report No. 379, Rev. 0, January 2003 Page 48 of 54

49 ZAT-Report No. 379, Rev. 0, January 2003 Page 49 of 54 Literature [1] A. Tokuhiro Natural Convection Heat Transfer Enhancement in Mercury with Gas Injection and in the Presence of a Transverse Magnetic Field PH.D. Thesis Purdue University, West Lafayette, IN (1991) [2] FLUENT Documentation FLUENT Incorporated [3] G.D. Mallinson and G. de Vahl Davis Three-dimensional natural convection in a box: a numverical study J. Fluid Mech., 83(1), 1-31 (1977) [4] H.Cords A literature survey on fluid flow data for mercury ESS T, 1998 [5] D. Choudhury Introduction to the Renormalization Group Method and Turbulence Modeling. Fluent Inc. Technical Memorandum TM-107, [6] A. T. Tokuhiro, P. S. Lykoudis Natural convection heat transfer from a vertical plate I. Enhancement with gas injection Int. J. Heat Mass Transfer, Vol. 37, No. 6, pp (1994) [7] A. T. Tokuhiro, P. S. Lykoudis Natural convection heat transfer from a vertical plate II. With gas injection and transverse magnetic field Int. J. Heat Mass Transfer, Vol. 37, No. 6, pp (1994) [8] M. Uotani Natural Convection Heat Transfer in Thermally Stratified Liquid Metal Journal of Nuclear Science and Technology, 24 [6], pp (June 1987)

50 ZAT-Report No. xxx, Rev. 0, March 2002 Page 50 of 50 Benchmark Activity on the TEFLU Sodium Jet Experiment

51 ZAT-Report No. 379, Rev. 0, January 2003 Page 51 of 54 List of Figures Figure 1: Experimental set-up... 6 Figure 2: Perspective view of experimental set-up with gas injection tubes... 7 Figure 3: CFD model... 8 Figure 4: Velocity distribution for the three- and two-dimensional model for load case W4Q0 (laminar viscous model) Figure 5: Figure 6: Figure 7: Figure 8: Figure 9: Temperature distribution for the three- and two-dimensional model for load case W4Q0 (laminar viscous model) Local Nusselt numbers as a function of the modified local Boussinesq number for load case W4Q Velocity distribution for the three- and two-dimensional model for load case W160Q0 (RNG k-ε model) Temperature distribution for the three- and two-dimensional model for load case W160Q0 (RNG k-ε model) Local Nusselt numbers as a function of the modified local Boussinesq number for load case W160Q Figure 10: Bulk temperature (difference to the mid-point temperature) as a function of the vertical distance to the leading edge for load case W4Q Figure 11: Velocity distribution for the test arrangement according to [8] after 180 s (heat flux: 370 W/m², laminar viscous model) Figure 12: Temperature distribution for the test arrangement according to [8] after 180 s (heat flux: 370 W/m², laminar viscous model) Figure 13: Bulk temperature as a function of the vertical distance to the leading edge for the test arrangement according to [8] Figure 14: Local Nusselt number as a function of the modified local Boussinesq number for the test arrangement according to [8] Figure 15: Velocity distribution for the test arrangement according to [8] after 3600 s (heat flux: 370 W/m², laminar viscous model) Figure 16: Temperature distribution for the test arrangement according to [8] after 3600 s (heat flux: 370 W/m², laminar viscous model) Figure 17: Velocity distribution for the RNG k-ε model (load case W4Q0) Figure 18: Temperature distribution for the RNG k-ε model (load case W4Q0) Figure 19: Local Nusselt number as a function of the modified local Boussinesq number for the laminar model and the RNG k-ε model (load case W4Q0) Figure 20: Local Nusselt number as a function of the modified local Boussinesq number for the laminar model and the RNG k-ε model (load case W10Q0)... 23

52 ZAT-Report No. 379, Rev. 0, January 2003 Page 52 of 54 Figure 21: Local Nusselt number as a function of the modified local Boussinesq number for heat-flux cases W40, W80 and W160 compared to the experimental results Figure 22: Bulk temperature (difference to the mid-point temperature) as a function of the vertical distance to the leading edge Figure 23: Velocity distribution within the cell for load case W10, Q Figure 24: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W10, Q Figure 25: Velocity distribution within the cell for load case W40, Q Figure 26: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W40, Q Figure 27: Velocity distribution within the cell for load case W80, Q Figure 28: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W80, Q Figure 29: Velocity distribution within the cell for load case W160, Q Figure 30: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W160, Q Figure 31: Void fraction profiles for a path perpendicular to the heated wall and 11 cm above the leading edge (load case W10Q43) Figure 32: Bubble velocity profiles for a path perpendicular to the heated wall and 11 cm above the leading edge (load case W10Q43) Figure 33: Calculated bubble and fluid velocity profiles for a path perpendicular to the heated wall and 11 cm above the leading edge (load case W10Q43) Figure 34: Local Nusselt numbers as a function of the modified local Boussinesq number for load case W10, Q0 and Q Figure 35: Local Nusselt number as a function of the modified local Boussinesq number for load case W4 with and without gas injection Figure 36: Local Nusselt number as a function of the modified local Boussinesq number for load case W10 with and without gas injection Figure 37: Local Nusselt number as a function of the modified local Boussinesq number for load case W40 with and without gas injection Figure 38: Local Nusselt number as a function of the modified local Boussinesq number for load case W80 with and without gas injection Figure 39: Local Nusselt number as a function of the modified local Boussinesq number for load case W160 with and without gas injection Figure 40: Bulk temperature (difference to the mid-point temperature) as a function of the vertical distance to the leading edge for load case W80 with and without bubble injection Figure 41: Bulk temperature as a function of the vertical distance to the leading edge for load case W

53 ZAT-Report No. 379, Rev. 0, January 2003 Page 53 of 54 Figure 42: Bulk temperature as a function of the vertical distance to the leading edge for load case W Figure 43: Bulk temperature as a function of the vertical distance to the leading edge for load case W Figure 44: Bulk temperature as a function of the vertical distance to the leading edge for load case W Figure 45: Bulk temperature as a function of the vertical distance to the leading edge for load case W Figure 46: Velocity distribution within the cell for load case W4, Q Figure 47: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W4, Q Figure 48: Velocity distribution within the cell for load case W10, Q Figure 49: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W10, Q Figure 50: Velocity distribution within the cell for load case W40, Q Figure 51: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W40, Q Figure 52: Velocity distribution within the cell for load case W80, Q Figure 53: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W80, Q Figure 54: Velocity distribution within the cell for load case W160, Q Figure 55: Temperature distribution (deviation to the mid-point temperature) within the cell for load case W160, Q Figure 56: Velocity distribution for the three- and two-dimensional model for load case W160Q43 (RNG k-ε model) Figure 57: Temperature distribution for the three- and two-dimensional model for load case W160Q43 (RNG k-ε model) Figure 58: Local Nusselt numbers as a function of the modified local Boussinesq number for load case W160Q

54 ZAT-Report No. 379, Rev. 0, January 2003 Page 54 of 54 List of Tables Table 1: Energy boundary conditions... 9 Table 2: Physical properties of mercury... 10