- Email: [email protected]
Theoretical analysis of recirculation zone and buffer zone in the ADS windowless spallation target
Annals of Nuclear Energy 77 (2015) 444–450
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Theoretical analysis of recirculation zone and buffer zone in the ADS windowless spallation target Jie Liu a,⇑, Chang-zhao Pan a,b, Jian-fei Tong c,d, Wen-qiang Lu a a
School of Physics, University of Chinese Academy of Sciences, Beijing, China Key Laboratory of Cryogenics, TIPC, Chinese Academy of Sciences, Beijing, China c China Spallation Neutron Source (CSNS), Institute of High Energy Physics (IHEP), Chinese Academy of Sciences (CAS), Dongguan, China d Dongguan Institute of Neutron Science (DINS), Dongguan, China b
a r t i c l e
i n f o
Article history: Received 10 April 2014 Received in revised form 4 December 2014 Accepted 7 December 2014
Keywords: Accelerator driven system (ADS) Windowless spallation target Lead–bismuth eutectic (LBE) Cavitation phase change Theoretical analysis Numerical simulation
a b s t r a c t The thermo-hydraulic analysis including reduction of the height of recirculation zone and stability of the free surface is very important in the design and optimization of ADS windowless spallation targets. In the present study, the Bernoulli equation is used to analyze the entire flow process in the target. Formulae for the height of the recirculation zone and the buffer zone are both obtained explicitly. Furthermore, numerical simulation for the heavy metal lead–bismuth eutectic liquid and vapor with cavitation phase change is also performed, and a novel method to calculate the height of the recirculation zone is put forward. By comparison of the theoretical formulae and numerical results, it is clearly shown that they agree with each other very well, and the heights predicted by the two methods are both determined by their own upstream flow parameters. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The accelerator driven system (ADS), aiming at the management and disposal of high level nuclear wastes, is the fundamental approach to reduce the minor actinides and long life fission products (Annex, 2005; Schuurmans et al., 2007). The spallation target is the ‘heart’ of the system, which carries away the extreme large power density because of the heat deposition and produces primary neutron source by the spallation reactions. In earlier designs, a window exists between proton beam and the target to ensure the safety of the accelerator. But the window has to sustain highenergy proton irradiation and corrosion by the flowing heavy liquid metal at very high temperature and no suitable materials can be used for a long time. Therefore, the windowless design is more desirable, which can avoid the mentioned problems (Bianchi et al., 2008). In the windowless target, thermo hydraulic design is very critical. Firstly, it is required to solve problems of flow instability and stable free surface can make little vapour enter vacuum tube where the proton beam travels. This problem can be solved by careful structural design and Batta and Class (2007, 2008) modified earlier target to yield a low free surface of the buffer zone to
⇑ Corresponding author. Tel.: +86 10 88256277. E-mail address: [email protected] (J. Liu). http://dx.doi.org/10.1016/j.anucene.2014.12.004 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
weaken fluctuations. Secondly, it is required to reduce or avoid recirculation flow. It may cause more heat deposition and will make more liquid be vapourized, which may threaten the safe operation of the accelerator. Through the help of the simulations of computational fluid dynamics (CFD) software, Roelofs et al. (2007, 2008a,b) designed and researched three feeder target, application of swirl and double inlet target, which can reduce the recirculation flow. The above two problems are the most key issues in the research and development of the ADS windowless spallation target (Tichelen et al., 2007). In experiment research, the temperature of the lead–bismuth eutectic (LBE) test facility must be kept very high to ensure that LBE is liquid state while it is difficult to be implemented. Water can be used to replace LBE as working fluid without taking heat transfer into account because they have similar hydraulic properties (Roelofs et al., 2008a). Therefore, it is convenient to build the water experiment to study the free surface behaviour and flow patterns (Su et al., 2012). Roelofs et al. (2008b) reviewed the development of ADS windowless spallation target in the experiment and the numerical simulation. Class et al. (2011) reviewed the thermo hydraulic development of XT-ADS and proposed some design principles. However, their results are all qualitatively and there is no quantitative criterion to calculate the height of the recirculation zone and the buffer zone. Therefore, the present paper’s main objective is to obtain the formulae which can be applied to calculate and evaluate the
445
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
recirculation zone and the buffer zone. In the first part, the Bernoulli’s equation is used to analyse flow of the liquid in the windowless target which has been separated into five parts and the formulae of the height of the recirculation zone and the buffer zone is deduced explicitly. In the second part, numerical simulation is employed to simulate the flowing process with cavitation phase change. At last, the theoretical formulas are compared and validated by the numerical results and conclusions are made. 2. Theoretical analysis Based on the EUROTRANS project (Annex, 2005; Roelofs et al., 2008c), the windowless spallation target can be split into five main parts, which are feeder line, target nozzle, accelerating zone, recirculation zone and buffer zone (Fig. 1). R0, R1, H1, H2 and a is the radius of the outer and inner cylindrical pipe, the height of the outer and inner cylindrical pipe, the convergence angle, respectively. These five parameters will greatly determine the flowing characteristics in the windowless target. In condition of steady-state flow and high Reynolds number, the Navier–Stokes (N–S) equation can be simplified into the Bernoulli’s equation according to Class et al. (2011). It can be used to analyze the flowing process of fluid in target:
p
q
þ
1 2 p0 1 v þ gz ¼ þ v 02 ð1 þ fÞ þ gz0 2 q 2
ð1Þ
where p is the static pressure, q is the density, v is the average velocity, g is the acceleration of the gravity, z is the height, and f is the pressure loss coefficient, 0 denotes the parameter of other location. Based on Eq. (1), Class et al. (2011) analyzed the reason to use the drag enhance in the feeder line and the target zone and also qualitatively explained the cause of the recirculation flow. In the following sections, the Eq. (1) is used to study in detail the flow of each part from the surface 0 (inlet) to the surface 5 (low outlet) and the formulae of the height of the recirculation zone and the buffer zone will be obtained in the end.
Dp ¼ f
ð3Þ
where f denotes the coefficient of the friction, Re is the Reynolds number, Dp is the pressure drop. The mass conservation equation gives the relationship for the height of the feeder line is very short and can be omitted:
v0 ¼ v1
ð4Þ
where 0 and 1 are at entrance and exit of the feeder line respectively. So it is convenient to start from target nozzle and use above equation to calculate the inlet’s state. Because point 2 is on the free surface and connected with vacuum tube, its pressure approximately equals to zero. Along the streamline 1–2, the Bernoulli’s equation can be simplified into the following form (Class et al., 2011):
1 2 p 1 v ð1 þ n12 Þ þ gz2 ¼ 1 þ v 21 þ gz1 2 2 q 2
ð5Þ
Then the mass conservation equation can be used to build the relationship between v1 and v2 which represent the average velocity at the entrance and exit of the nozzle, yields:
A1 v 1 ¼ A2 v 2
ð6Þ
where A1 and A2 are the area of the entrance and exit of the target nozzle:
A1 ¼ pðR20 R21 Þ
ð7Þ
A2 ¼ pðR22 R21 Þ
ð8Þ
where R2 (Fig. 2) can be calculated:
R2 ¼ R0 ðH2 H1 Þ tan a
ð9Þ
Combining Eqs. (7)–(9) into Eq. (6) and yields:
v2 ¼
2.1. Target nozzle
R20 R21 ½R0 ðH2 H1 Þ tan a2 R21
v1
ð10Þ
Therefore, Eq. (5) can be written in the following form:
Because the section of the feeder line is the concentric tube flow, it can be described by pipe correlation (Batta and Class, 2007; Mcadams, 1954):
f ¼ 0:04Re0:2
H1 qv 20 4ðR0 R1 Þ 2
ð2Þ
9 8" #2 = 1< R20 R21 ¼ ð1 þ n12 Þ 1 v 21 2 2 ; q 2 : ½R0 ðH2 H1 Þ tan a R1
p1
þ gðz2 z1 Þ
Fig. 1. The latest structure of the windowless spallation target of the EUROTRANS project (Class et al., 2011).
ð11Þ
446
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
It is required that the inlet pressure is bigger than the saturated vapor pressure so that the entrance of target nozzle does not produce the cavitation. Because z2 is less than z1, enhancing the pressure loss coefficient f1–2 is a good way to satisfy p1 > 0 (Class et al., 2011). Variations of the other structural parameters such as R0, R1, H1 and H2 can also guarantee this demand. 2.2. Accelerating zone The fluid is accelerated by the force of the gravity in this zone. Assuming there is no pressure drop and the pressure approximately equals to zero at the free surface (p2 p3 0) which is connected with vacuum tube. Along the streamline on the free surface (Fig. 1(a), line3), the Bernoulli’s equation can be simplified into the following form:
1 2 1 2 v ¼ v þ gðz2 z3 Þ 2 3 2 2
ð12Þ
In the above equation, z3 is an unknown parameter. It can be calculated:
z2 z3 ¼ R1 = tan h
ð13Þ
where h is defined as the convergence angle (Fig. 2) and is also determined by structural parameters. Combining Eqs. (10), (12) and (13), then v3 can be easily obtained:
v3
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi #2 u" u R20 R21 t ¼ v 21 þ 2gR1 = tan h ½R0 ðH2 H1 Þ tan a2 R21
ð14Þ
Fig. 2. Enlarged schematic of the accelerating zone and the recirculation zone.
3–4, the Bernoulli’s equation can be simplified into the following form:
p4
q
þ
1 2 1 2 v ¼ v 2 4 2 3
ð19Þ
The relationship between v 3 and v 4 can be determined via the equation of momentum conservation:
v 4 ¼ v 3 cos h
ð20Þ
Therefore, combining Eqs. (14), (19) and (20) yields: 2.3. Recirculation zone Assuming the average velocities of can be obtained:
p
ðR22
R21 Þ
¼p
ðR23
v2 and v2
0
do not change, it
R24 Þ
ð21Þ ð15Þ
The following equations are derived using the relationship of the structural parameters:
R1 R4 H3
ð16Þ
R3 ¼ R0 ðH2 þ H3 H1 Þ tan a
ð17Þ
h ¼ tan
1
8" 9 #2 < = 1 R20 R21 2 2 p4 ¼ q sin h v 1 þ 2gR1 = tan h; 2 2 : 2 ½R0 ðH2 H1 Þ tan a R1
This p4 needs hydrostatic pressure to keep balance:
p4 ¼ qgHre
ð22Þ
So the height of recirculation zone (Fig. 3):
8" 9 #2 < = 1 R20 R21 2 2 Hre ¼ sin h v 1 þ 2gR1 = tan h; 2 2 : 2g ½R0 ðH2 H1 Þ tan a R1 ð23Þ
Therefore, combining Eqs. (9), (15) and (17) into Eq. (16):
h ¼ tan1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R1 ½R0 ðH2 þ H3 H1 Þ tan a2 þ R21 ½R0 ðH2 H1 Þ tan a2 =H3
In the latest structure of windowless spallation target of EUROTRANS project (Class et al., 2011), the convergence angle is 11.3°. The computed result of Eq. (18) will be a little smaller than the reality because the pressure drop is not taken into account. Considering the linear pressure drop, a correction coefficient should be added to the right side of Eq. (15). According to Du (2007), the correction coefficient is chosen to be 0.98, so the convergence angle is 11.689°. The accelerating zone will merge at the axis at the end. The fluid’s radial velocities reduce to zero and the pressure increases. So a recirculation flow forms because of this elevated pressure (Class et al., 2011). Point 3 and point 4 are very close to the merging point (Fig. 2). The point 3 is at the free surface and its pressure approximately equals to zero. Therefore, along the streamline
ð18Þ
Eq. (23) can be regarded as a criterion to evaluate the height of recirculation zone. Because the recirculation flow may cause the problem that the heat deposition cannot be taken away and the temperature will be higher and higher. Therefore, Hre should be designed as smaller as possible. It is clearly seen from the Eq. (23) that Hre is determined by the structural parameters such as h, R0, R1 and the inlet velocity and it has nothing to do with fluid properties. So it provides an explicit reference for the design and optimization of the experiment on water or liquid metal. 2.4. Buffer zone Along the streamline 4–5 in Fig. 4, assuming the flow crosssectional area of point 4 and point 5 do not change and the pressure drop can be ignored. Then:
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
447
Fig. 3. The height of recirculation zone. Fig. 4. Schematic of flow in the buffer zone.
p5
q
¼
p4
q
þ gz4
ð24Þ
where p5 is not the real outlet pressure. The real pressure is pout and can be calculated:
pout
q
þ
1 2 p4 1 2 v ¼ þ v 4 þ gz4 2 5 q 2
ð25Þ
If p5 > pout and according to Eqs. (24) and (25), there must be
v 5 > v 4 . It means that the flow cross-sectional area of the exit is larger than that of the entrance according to the mass conservation. It does not conform to the real situation and p5 < pout is required, so:
pout
9 8" #2 = < 1 R20 R21 2 2 > q sin h v 1 þ 2gR1 = tan h; 2 2 : 2 ½R0 ðH2 H1 Þ tan a R1 þ qgz4
ð26Þ Eq. (26) means that the area of the flow cross-section increases when the fluid flows to the low outlet (Fig. 4). Furthermore, assuming the velocity varies linearly, the outlet velocity can be obtained:
v out ¼
v back v 5 R0
r þ v5
ð27Þ
The mass of the vapor is ignored:
v 1 pðR20 R21 Þ ¼
Z
R0
2v out prdr
ð28Þ
0
So the height of the buffer zone can be got:
gHbu ¼
pout
q
1 2 v 2 back
ð29Þ
Combining Eqs. (25) and (27)–(29) yields:
Hbu
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#2 " ! pout 1 3 R21 1 2ðp4 pout Þ ¼ v 1 2 þ v 24 þ 2gz4 2 qg 2g 2 1 q R0 ð30Þ
of fluid (VOF) (Harlow and Welch, 1965; Hirt and Nichols, 1981) combining with the cavitation is an appropriate numerical model to capture the free surface. The VOF methodology is a common method to solve the free surface problem. It defines a function F whose value is unity at any point occupied by fluid and zero otherwise (Hirt and Nichols, 1981). Cells with F values between zero and one contain a free surface between the liquid and the vapour. Therefore, this work employs the k–e turbulence model, the VOF method and the cavitation model to simulate the flow in the target. In order to decrease the computational cost, a 2D symmetrical flow domain is used. Quadrilateral mesh is used to discrete the computational domain, which totally contains 28,425 cells. PISO algorithm (Tong et al., 2003) is applied to solve this unsteady problem. At the initial state, the entire target is filled with the liquid. The boundary conditions are given in Table 1. For validating the model, water is chosen as the working fluid. Fig. 5 shows that the phase distribution in the simulation is coincident with the result reported by Batta and Class (2008). Therefore, this model is suitable for simulating the flow in the target. The real working liquid is LBE and the density of liquid LBE is almost ten times bigger than that of water. So the low outlet gauge pressure is set nearly ten times bigger. According to the actual physical process, the properties of LBE liquid and vapour in Table 2 are calculated at temperature 723 K and 1450 K, respectively. It is clearly shown in Fig. 6 the gradient of the pressure is formed uniformly on the low outlet which makes liquid be steady. Moreover, the pressure of merging point is the highest in its near field and also beginning of the recirculation zone. Fig. 7 shows the height of the recirculation zone increases as increasing inlet velocity while keeps constant as increasing low outlet pressure. It means that the height of the recirculation zone is only affected by upstream flow from the inlet to the merging point.
4. Comparison of the theoretical formulae and the numerical results
3. Numerical simulation
4.1. Height of the recirculation zone
This work employs numerical simulation to study the flow in the target. According to the work by Batta and Class (2008), volume
Fig. 8 shows the density and static pressure of the mixture including the LBE liquid and vapor on the axis which the pressure
448
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
Table 1 Boundary conditions and cavitation pressure. Working fluid
Inlet velocity (m/s)
Low outlet pressure (Pa)
Up outlet pressure (Pa)
Cavitation pressure (Pa)
Water LBE
0.876 0.8/0.9/1.0/1.1/1.2
5330 24330/26330/28330
2330 2330
2370 2370
Fig. 5. The phase distribution at the steady state (left figure is the result of this paper, right figure is the result of Batta and Class, 2008).
of the low outlet is set as 24,330 Pa and the inlet velocity is set as 1.0 m/s in the numerical simulation. The density is changed from the density of the LBE liquid to the density of LBE vapor. The position of the merging point can be determined by its highest static pressure. The highest position of the recirculation zone can be determined by the location where the density is changed from the liquid to the vapor. Therefore, the height of the recirculation zone equals to the distance between the merging point and the density junction point. The comparison between the numerical results and theoretical formulae of the height of the recirculation zone are shown in Fig. 9. It depicts that as the inlet velocity increases the height of the recirculation zone increases. So the smaller inlet velocity, the shorter the height is. The relative errors of the numerical results and theoretical correction formulae (regarding the convergence angle as 11.689°) are within the range of 2%. Fig. 10 shows that the height of the recirculation zone keeps constant as the low outlet pressure increases. So the low outlet pressure has no influence on the height of the recirculation zone. This also can be seen in Eq. (23), because
Fig. 6. The distribution of phase (left) and total pressure (right).
there is no term which has the relationship with the low outlet pressure. The correctness of the Eq. (23) is proved by the comparison. Therefore, the height of the recirculation zone can be optimized through designing the structure carefully and adjusting the inlet velocity according to it. 4.2. Height of the buffer zone According to Eq. (26), the pressure boundary pout is bigger than p5 . So the velocity reverses its flowing direction in the low outlet. Therefore, the dynamic pressure assumes to be lost, and the pressure loss coefficient equals to 1.0 in Eq. (29). Basing on this, the comparison between the numerical results and theoretical formulae of the height of the buffer zone is shown in Figs. 11 and 12. Fig. 11 shows the height of the buffer zone decreases as the inlet velocity increases. The relative errors between the numerical and theoretical correction results are within the range of 5%. However, as the low outlet pressure increases the height of the buffer zone will increase. Therefore, the height of the buffer zone is determined
Table 2 Thermo physical properties of LBE liquid and vapor (Sobolev, 2007). LBE properties
Equations
Values
Unit
Density of liquid Viscosity of liquid
11; 096 1:3236 T
10,139 1.4 103
kg/m3 Pa s
Saturated pressure Density of vapora Viscosity of vapor a
Approximate from the pure lead.
4:94 104 e754:1=T 1:11 1010 e22552=T 1:939 þ 0:00149 T 4
14:43T 0:5 =ð0:003T 0:15 þ 8:5e1:410
T
þ 35:1e4:310
4
T
Þ
2370
Pa
0.2215 5.322 105
kg/m3 Pa s
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
449
Fig. 7. Influence on the height of the recirculation zone by: (a) the inlet velocity; (b) the low outlet pressure.
Fig. 8. Schematic (a) and enlarged view (b) of the density and the static pressure on the axis.
Fig. 9. The height of the recirculation zone varies with the inlet velocity.
Fig. 10. The height of the recirculation zone varies with the low outlet pressure.
450
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
zone according to distribution of the density and static pressure on the symmetry axis. The theoretical formulae and numerical results show that they coincide with each other very well and prove the correctness of mathematical deduction of the theoretical formulae. The height of the recirculation zone has nothing to do with the fluid properties and low outlet pressure while it increases with the increasing inlet velocity. But the height of the buffer zone increases with the reduction of inlet velocity and increase of low outlet pressure. The comparison also reveals the two heights are greatly determined by their upstream flow, respectively. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 51276190). References
Fig. 11. The height of the buffer zone varies with the inlet velocity.
Fig. 12. The height of the buffer zone varies with the low outlet pressure.
by the inlet velocity, the target structure and the low outlet pressure. 5. Conclusions The present study uses the Bernoulli’s equation to analyze theoretically the whole flowing process in the ADS windowless spallation target and performs the numerical simulation for LBE liquid and vapour using the CFD simulation. In the theoretical analysis, the formulae for the height of the recirculation zone and the buffer zone are both acquired and can be used to guide the design or optimization of the target. In the numerical study, a novel method is put forward to calculate the height of the recirculation
Annex, I., 2005. EUROpean Research Programme for the TRANSmutation of High Level Nuclear Waste in an Accelerator Driven System, Project acronym: EUROTRANS, Contract no.: FI6W-CT-2004-516520. Batta, A., Class, A., 2007. Numerical investigations on geometrical designs of the windowless XT ADS spallation target. In: International Conference on Advances in Nuclear Power Plants (ICAPP 2007), Nice, France. Batta, A., Class, A., 2008. Free surface modeling and simulation of the water experiment for the XT ADS spallation target. In: Proceedings of the 2008 International Congress on Advances in Nuclear Power Plants. Anaheim, California. Bianchi, F., Ferri, R., Moreau, V., 2008. Thermo-hydraulic analysis of the windowless target system. Nucl. Eng. Des. 238, 2135–2145. Class, A.G., Angeli, D., Batta, A., Dierckx, M., Fellmoser, F., Moreau, V., Roelofs, F., Schuurmans, P., Van Tichelen, K., Wetzel, T., 2011. XT-ADS Windowless spallation target thermohydraulic design & experimental setup. J. Nucl. Mater. 415, 378–384. Du, G.S., 2007. Engineering Fluid Mechanics. China Electric Power Press. Harlow, F.H., Welch, J.E., 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225. Mcadams, W.H., 1954. Heat Transmission. McGraw-Hill Press. Roelofs, F., Siccama, N.B., Willemsen, S.M., 2007. Development of an Euler–Euler two-phase model for application in the windowless XT-ADS spallation target design. In: International Conference on Advances in Nuclear Power Plants (ICAPP 2007), Nice, France, p. 7092. Roelofs, F., Siccama, N.B., de Jager, B., van Tichelen, K., Dierckx, M., Heyse, J., Rosseel, K., Schuurmans, P., 2008a. Comparison of the hydraulics in concentric and three feeder XT-ADS windowless spallation target designs. In: Proceedings of ICAPP’08, Anaheim, USA, p. 8029. Roelofs, F., Siccama, N.B., Jeanmart, H., Tichelen, K.V., Dierckx, M., Schuurmans, P., 2008b. Application of a controlled swirl in the XT-ADS spallation target. In: International Conference on Advances in Nuclear Power Plants Anaheim, USA, p. 7029. Roelofs, F., de Jager, B., Class, A., Jeanmart, H., Schuurmans, P., Ciampichetti, A., Gerbeth, G., Stieglitz, R., Fazio, C., 2008c. European research on HLM thermalhydraulics for ADS applications. J. Nucl. Mater. 376, 401–404. Schuurmans, P., Guertin, A., Buhour, J.M., Cadiou, A., Dierckx, M., Heyse, J., Rosseel, K., Van Tichelen, K., Stieglitz, R., Coors, D., 2007. Design and R&D support of the XT-ADS spallation target. In: Utilisation and Reliability of High Power Proton Accelerators (HPPA5), p. 245. Sobolev, V., 2007. Thermophysical properties of lead and lead–bismuth eutectic. J. Nucl. Mater. 362, 235–247. Su, G.Y., Gu, H.Y., Cheng, X., 2012. Experimental and numerical studies on free surface flow of windowless target. Ann. Nucl. Energy 43, 142–149. Tichelen, K.V., Kupschus, P., Arien, B., Abderrahim, H.A., 2007. Design and verification experiments for the windowless spallation target of the ADS prototype MYRRHA. In: Nuclear Science Utilisation and Reliability of High Power Proton Accelerators: Workshop Proceedings, Mol, Belgium, p. 311–325. Tong, W., Chuang-ang, G., Bo, Y., Jian-de, H., 2003. PISO algorithm for unsteady flow field. J. Hydrodyn. 18, 233–239.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Theoretical analysis of recirculation zone and buffer zone in the ADS windowless spallation target Jie Liu a,⇑, Chang-zhao Pan a,b, Jian-fei Tong c,d, Wen-qiang Lu a a
School of Physics, University of Chinese Academy of Sciences, Beijing, China Key Laboratory of Cryogenics, TIPC, Chinese Academy of Sciences, Beijing, China c China Spallation Neutron Source (CSNS), Institute of High Energy Physics (IHEP), Chinese Academy of Sciences (CAS), Dongguan, China d Dongguan Institute of Neutron Science (DINS), Dongguan, China b
a r t i c l e
i n f o
Article history: Received 10 April 2014 Received in revised form 4 December 2014 Accepted 7 December 2014
Keywords: Accelerator driven system (ADS) Windowless spallation target Lead–bismuth eutectic (LBE) Cavitation phase change Theoretical analysis Numerical simulation
a b s t r a c t The thermo-hydraulic analysis including reduction of the height of recirculation zone and stability of the free surface is very important in the design and optimization of ADS windowless spallation targets. In the present study, the Bernoulli equation is used to analyze the entire flow process in the target. Formulae for the height of the recirculation zone and the buffer zone are both obtained explicitly. Furthermore, numerical simulation for the heavy metal lead–bismuth eutectic liquid and vapor with cavitation phase change is also performed, and a novel method to calculate the height of the recirculation zone is put forward. By comparison of the theoretical formulae and numerical results, it is clearly shown that they agree with each other very well, and the heights predicted by the two methods are both determined by their own upstream flow parameters. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The accelerator driven system (ADS), aiming at the management and disposal of high level nuclear wastes, is the fundamental approach to reduce the minor actinides and long life fission products (Annex, 2005; Schuurmans et al., 2007). The spallation target is the ‘heart’ of the system, which carries away the extreme large power density because of the heat deposition and produces primary neutron source by the spallation reactions. In earlier designs, a window exists between proton beam and the target to ensure the safety of the accelerator. But the window has to sustain highenergy proton irradiation and corrosion by the flowing heavy liquid metal at very high temperature and no suitable materials can be used for a long time. Therefore, the windowless design is more desirable, which can avoid the mentioned problems (Bianchi et al., 2008). In the windowless target, thermo hydraulic design is very critical. Firstly, it is required to solve problems of flow instability and stable free surface can make little vapour enter vacuum tube where the proton beam travels. This problem can be solved by careful structural design and Batta and Class (2007, 2008) modified earlier target to yield a low free surface of the buffer zone to
⇑ Corresponding author. Tel.: +86 10 88256277. E-mail address: [email protected] (J. Liu). http://dx.doi.org/10.1016/j.anucene.2014.12.004 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
weaken fluctuations. Secondly, it is required to reduce or avoid recirculation flow. It may cause more heat deposition and will make more liquid be vapourized, which may threaten the safe operation of the accelerator. Through the help of the simulations of computational fluid dynamics (CFD) software, Roelofs et al. (2007, 2008a,b) designed and researched three feeder target, application of swirl and double inlet target, which can reduce the recirculation flow. The above two problems are the most key issues in the research and development of the ADS windowless spallation target (Tichelen et al., 2007). In experiment research, the temperature of the lead–bismuth eutectic (LBE) test facility must be kept very high to ensure that LBE is liquid state while it is difficult to be implemented. Water can be used to replace LBE as working fluid without taking heat transfer into account because they have similar hydraulic properties (Roelofs et al., 2008a). Therefore, it is convenient to build the water experiment to study the free surface behaviour and flow patterns (Su et al., 2012). Roelofs et al. (2008b) reviewed the development of ADS windowless spallation target in the experiment and the numerical simulation. Class et al. (2011) reviewed the thermo hydraulic development of XT-ADS and proposed some design principles. However, their results are all qualitatively and there is no quantitative criterion to calculate the height of the recirculation zone and the buffer zone. Therefore, the present paper’s main objective is to obtain the formulae which can be applied to calculate and evaluate the
445
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
recirculation zone and the buffer zone. In the first part, the Bernoulli’s equation is used to analyse flow of the liquid in the windowless target which has been separated into five parts and the formulae of the height of the recirculation zone and the buffer zone is deduced explicitly. In the second part, numerical simulation is employed to simulate the flowing process with cavitation phase change. At last, the theoretical formulas are compared and validated by the numerical results and conclusions are made. 2. Theoretical analysis Based on the EUROTRANS project (Annex, 2005; Roelofs et al., 2008c), the windowless spallation target can be split into five main parts, which are feeder line, target nozzle, accelerating zone, recirculation zone and buffer zone (Fig. 1). R0, R1, H1, H2 and a is the radius of the outer and inner cylindrical pipe, the height of the outer and inner cylindrical pipe, the convergence angle, respectively. These five parameters will greatly determine the flowing characteristics in the windowless target. In condition of steady-state flow and high Reynolds number, the Navier–Stokes (N–S) equation can be simplified into the Bernoulli’s equation according to Class et al. (2011). It can be used to analyze the flowing process of fluid in target:
p
q
þ
1 2 p0 1 v þ gz ¼ þ v 02 ð1 þ fÞ þ gz0 2 q 2
ð1Þ
where p is the static pressure, q is the density, v is the average velocity, g is the acceleration of the gravity, z is the height, and f is the pressure loss coefficient, 0 denotes the parameter of other location. Based on Eq. (1), Class et al. (2011) analyzed the reason to use the drag enhance in the feeder line and the target zone and also qualitatively explained the cause of the recirculation flow. In the following sections, the Eq. (1) is used to study in detail the flow of each part from the surface 0 (inlet) to the surface 5 (low outlet) and the formulae of the height of the recirculation zone and the buffer zone will be obtained in the end.
Dp ¼ f
ð3Þ
where f denotes the coefficient of the friction, Re is the Reynolds number, Dp is the pressure drop. The mass conservation equation gives the relationship for the height of the feeder line is very short and can be omitted:
v0 ¼ v1
ð4Þ
where 0 and 1 are at entrance and exit of the feeder line respectively. So it is convenient to start from target nozzle and use above equation to calculate the inlet’s state. Because point 2 is on the free surface and connected with vacuum tube, its pressure approximately equals to zero. Along the streamline 1–2, the Bernoulli’s equation can be simplified into the following form (Class et al., 2011):
1 2 p 1 v ð1 þ n12 Þ þ gz2 ¼ 1 þ v 21 þ gz1 2 2 q 2
ð5Þ
Then the mass conservation equation can be used to build the relationship between v1 and v2 which represent the average velocity at the entrance and exit of the nozzle, yields:
A1 v 1 ¼ A2 v 2
ð6Þ
where A1 and A2 are the area of the entrance and exit of the target nozzle:
A1 ¼ pðR20 R21 Þ
ð7Þ
A2 ¼ pðR22 R21 Þ
ð8Þ
where R2 (Fig. 2) can be calculated:
R2 ¼ R0 ðH2 H1 Þ tan a
ð9Þ
Combining Eqs. (7)–(9) into Eq. (6) and yields:
v2 ¼
2.1. Target nozzle
R20 R21 ½R0 ðH2 H1 Þ tan a2 R21
v1
ð10Þ
Therefore, Eq. (5) can be written in the following form:
Because the section of the feeder line is the concentric tube flow, it can be described by pipe correlation (Batta and Class, 2007; Mcadams, 1954):
f ¼ 0:04Re0:2
H1 qv 20 4ðR0 R1 Þ 2
ð2Þ
9 8" #2 = 1< R20 R21 ¼ ð1 þ n12 Þ 1 v 21 2 2 ; q 2 : ½R0 ðH2 H1 Þ tan a R1
p1
þ gðz2 z1 Þ
Fig. 1. The latest structure of the windowless spallation target of the EUROTRANS project (Class et al., 2011).
ð11Þ
446
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
It is required that the inlet pressure is bigger than the saturated vapor pressure so that the entrance of target nozzle does not produce the cavitation. Because z2 is less than z1, enhancing the pressure loss coefficient f1–2 is a good way to satisfy p1 > 0 (Class et al., 2011). Variations of the other structural parameters such as R0, R1, H1 and H2 can also guarantee this demand. 2.2. Accelerating zone The fluid is accelerated by the force of the gravity in this zone. Assuming there is no pressure drop and the pressure approximately equals to zero at the free surface (p2 p3 0) which is connected with vacuum tube. Along the streamline on the free surface (Fig. 1(a), line3), the Bernoulli’s equation can be simplified into the following form:
1 2 1 2 v ¼ v þ gðz2 z3 Þ 2 3 2 2
ð12Þ
In the above equation, z3 is an unknown parameter. It can be calculated:
z2 z3 ¼ R1 = tan h
ð13Þ
where h is defined as the convergence angle (Fig. 2) and is also determined by structural parameters. Combining Eqs. (10), (12) and (13), then v3 can be easily obtained:
v3
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi #2 u" u R20 R21 t ¼ v 21 þ 2gR1 = tan h ½R0 ðH2 H1 Þ tan a2 R21
ð14Þ
Fig. 2. Enlarged schematic of the accelerating zone and the recirculation zone.
3–4, the Bernoulli’s equation can be simplified into the following form:
p4
q
þ
1 2 1 2 v ¼ v 2 4 2 3
ð19Þ
The relationship between v 3 and v 4 can be determined via the equation of momentum conservation:
v 4 ¼ v 3 cos h
ð20Þ
Therefore, combining Eqs. (14), (19) and (20) yields: 2.3. Recirculation zone Assuming the average velocities of can be obtained:
p
ðR22
R21 Þ
¼p
ðR23
v2 and v2
0
do not change, it
R24 Þ
ð21Þ ð15Þ
The following equations are derived using the relationship of the structural parameters:
R1 R4 H3
ð16Þ
R3 ¼ R0 ðH2 þ H3 H1 Þ tan a
ð17Þ
h ¼ tan
1
8" 9 #2 < = 1 R20 R21 2 2 p4 ¼ q sin h v 1 þ 2gR1 = tan h; 2 2 : 2 ½R0 ðH2 H1 Þ tan a R1
This p4 needs hydrostatic pressure to keep balance:
p4 ¼ qgHre
ð22Þ
So the height of recirculation zone (Fig. 3):
8" 9 #2 < = 1 R20 R21 2 2 Hre ¼ sin h v 1 þ 2gR1 = tan h; 2 2 : 2g ½R0 ðH2 H1 Þ tan a R1 ð23Þ
Therefore, combining Eqs. (9), (15) and (17) into Eq. (16):
h ¼ tan1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R1 ½R0 ðH2 þ H3 H1 Þ tan a2 þ R21 ½R0 ðH2 H1 Þ tan a2 =H3
In the latest structure of windowless spallation target of EUROTRANS project (Class et al., 2011), the convergence angle is 11.3°. The computed result of Eq. (18) will be a little smaller than the reality because the pressure drop is not taken into account. Considering the linear pressure drop, a correction coefficient should be added to the right side of Eq. (15). According to Du (2007), the correction coefficient is chosen to be 0.98, so the convergence angle is 11.689°. The accelerating zone will merge at the axis at the end. The fluid’s radial velocities reduce to zero and the pressure increases. So a recirculation flow forms because of this elevated pressure (Class et al., 2011). Point 3 and point 4 are very close to the merging point (Fig. 2). The point 3 is at the free surface and its pressure approximately equals to zero. Therefore, along the streamline
ð18Þ
Eq. (23) can be regarded as a criterion to evaluate the height of recirculation zone. Because the recirculation flow may cause the problem that the heat deposition cannot be taken away and the temperature will be higher and higher. Therefore, Hre should be designed as smaller as possible. It is clearly seen from the Eq. (23) that Hre is determined by the structural parameters such as h, R0, R1 and the inlet velocity and it has nothing to do with fluid properties. So it provides an explicit reference for the design and optimization of the experiment on water or liquid metal. 2.4. Buffer zone Along the streamline 4–5 in Fig. 4, assuming the flow crosssectional area of point 4 and point 5 do not change and the pressure drop can be ignored. Then:
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
447
Fig. 3. The height of recirculation zone. Fig. 4. Schematic of flow in the buffer zone.
p5
q
¼
p4
q
þ gz4
ð24Þ
where p5 is not the real outlet pressure. The real pressure is pout and can be calculated:
pout
q
þ
1 2 p4 1 2 v ¼ þ v 4 þ gz4 2 5 q 2
ð25Þ
If p5 > pout and according to Eqs. (24) and (25), there must be
v 5 > v 4 . It means that the flow cross-sectional area of the exit is larger than that of the entrance according to the mass conservation. It does not conform to the real situation and p5 < pout is required, so:
pout
9 8" #2 = < 1 R20 R21 2 2 > q sin h v 1 þ 2gR1 = tan h; 2 2 : 2 ½R0 ðH2 H1 Þ tan a R1 þ qgz4
ð26Þ Eq. (26) means that the area of the flow cross-section increases when the fluid flows to the low outlet (Fig. 4). Furthermore, assuming the velocity varies linearly, the outlet velocity can be obtained:
v out ¼
v back v 5 R0
r þ v5
ð27Þ
The mass of the vapor is ignored:
v 1 pðR20 R21 Þ ¼
Z
R0
2v out prdr
ð28Þ
0
So the height of the buffer zone can be got:
gHbu ¼
pout
q
1 2 v 2 back
ð29Þ
Combining Eqs. (25) and (27)–(29) yields:
Hbu
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#2 " ! pout 1 3 R21 1 2ðp4 pout Þ ¼ v 1 2 þ v 24 þ 2gz4 2 qg 2g 2 1 q R0 ð30Þ
of fluid (VOF) (Harlow and Welch, 1965; Hirt and Nichols, 1981) combining with the cavitation is an appropriate numerical model to capture the free surface. The VOF methodology is a common method to solve the free surface problem. It defines a function F whose value is unity at any point occupied by fluid and zero otherwise (Hirt and Nichols, 1981). Cells with F values between zero and one contain a free surface between the liquid and the vapour. Therefore, this work employs the k–e turbulence model, the VOF method and the cavitation model to simulate the flow in the target. In order to decrease the computational cost, a 2D symmetrical flow domain is used. Quadrilateral mesh is used to discrete the computational domain, which totally contains 28,425 cells. PISO algorithm (Tong et al., 2003) is applied to solve this unsteady problem. At the initial state, the entire target is filled with the liquid. The boundary conditions are given in Table 1. For validating the model, water is chosen as the working fluid. Fig. 5 shows that the phase distribution in the simulation is coincident with the result reported by Batta and Class (2008). Therefore, this model is suitable for simulating the flow in the target. The real working liquid is LBE and the density of liquid LBE is almost ten times bigger than that of water. So the low outlet gauge pressure is set nearly ten times bigger. According to the actual physical process, the properties of LBE liquid and vapour in Table 2 are calculated at temperature 723 K and 1450 K, respectively. It is clearly shown in Fig. 6 the gradient of the pressure is formed uniformly on the low outlet which makes liquid be steady. Moreover, the pressure of merging point is the highest in its near field and also beginning of the recirculation zone. Fig. 7 shows the height of the recirculation zone increases as increasing inlet velocity while keeps constant as increasing low outlet pressure. It means that the height of the recirculation zone is only affected by upstream flow from the inlet to the merging point.
4. Comparison of the theoretical formulae and the numerical results
3. Numerical simulation
4.1. Height of the recirculation zone
This work employs numerical simulation to study the flow in the target. According to the work by Batta and Class (2008), volume
Fig. 8 shows the density and static pressure of the mixture including the LBE liquid and vapor on the axis which the pressure
448
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
Table 1 Boundary conditions and cavitation pressure. Working fluid
Inlet velocity (m/s)
Low outlet pressure (Pa)
Up outlet pressure (Pa)
Cavitation pressure (Pa)
Water LBE
0.876 0.8/0.9/1.0/1.1/1.2
5330 24330/26330/28330
2330 2330
2370 2370
Fig. 5. The phase distribution at the steady state (left figure is the result of this paper, right figure is the result of Batta and Class, 2008).
of the low outlet is set as 24,330 Pa and the inlet velocity is set as 1.0 m/s in the numerical simulation. The density is changed from the density of the LBE liquid to the density of LBE vapor. The position of the merging point can be determined by its highest static pressure. The highest position of the recirculation zone can be determined by the location where the density is changed from the liquid to the vapor. Therefore, the height of the recirculation zone equals to the distance between the merging point and the density junction point. The comparison between the numerical results and theoretical formulae of the height of the recirculation zone are shown in Fig. 9. It depicts that as the inlet velocity increases the height of the recirculation zone increases. So the smaller inlet velocity, the shorter the height is. The relative errors of the numerical results and theoretical correction formulae (regarding the convergence angle as 11.689°) are within the range of 2%. Fig. 10 shows that the height of the recirculation zone keeps constant as the low outlet pressure increases. So the low outlet pressure has no influence on the height of the recirculation zone. This also can be seen in Eq. (23), because
Fig. 6. The distribution of phase (left) and total pressure (right).
there is no term which has the relationship with the low outlet pressure. The correctness of the Eq. (23) is proved by the comparison. Therefore, the height of the recirculation zone can be optimized through designing the structure carefully and adjusting the inlet velocity according to it. 4.2. Height of the buffer zone According to Eq. (26), the pressure boundary pout is bigger than p5 . So the velocity reverses its flowing direction in the low outlet. Therefore, the dynamic pressure assumes to be lost, and the pressure loss coefficient equals to 1.0 in Eq. (29). Basing on this, the comparison between the numerical results and theoretical formulae of the height of the buffer zone is shown in Figs. 11 and 12. Fig. 11 shows the height of the buffer zone decreases as the inlet velocity increases. The relative errors between the numerical and theoretical correction results are within the range of 5%. However, as the low outlet pressure increases the height of the buffer zone will increase. Therefore, the height of the buffer zone is determined
Table 2 Thermo physical properties of LBE liquid and vapor (Sobolev, 2007). LBE properties
Equations
Values
Unit
Density of liquid Viscosity of liquid
11; 096 1:3236 T
10,139 1.4 103
kg/m3 Pa s
Saturated pressure Density of vapora Viscosity of vapor a
Approximate from the pure lead.
4:94 104 e754:1=T 1:11 1010 e22552=T 1:939 þ 0:00149 T 4
14:43T 0:5 =ð0:003T 0:15 þ 8:5e1:410
T
þ 35:1e4:310
4
T
Þ
2370
Pa
0.2215 5.322 105
kg/m3 Pa s
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
449
Fig. 7. Influence on the height of the recirculation zone by: (a) the inlet velocity; (b) the low outlet pressure.
Fig. 8. Schematic (a) and enlarged view (b) of the density and the static pressure on the axis.
Fig. 9. The height of the recirculation zone varies with the inlet velocity.
Fig. 10. The height of the recirculation zone varies with the low outlet pressure.
450
J. Liu et al. / Annals of Nuclear Energy 77 (2015) 444–450
zone according to distribution of the density and static pressure on the symmetry axis. The theoretical formulae and numerical results show that they coincide with each other very well and prove the correctness of mathematical deduction of the theoretical formulae. The height of the recirculation zone has nothing to do with the fluid properties and low outlet pressure while it increases with the increasing inlet velocity. But the height of the buffer zone increases with the reduction of inlet velocity and increase of low outlet pressure. The comparison also reveals the two heights are greatly determined by their upstream flow, respectively. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 51276190). References
Fig. 11. The height of the buffer zone varies with the inlet velocity.
Fig. 12. The height of the buffer zone varies with the low outlet pressure.
by the inlet velocity, the target structure and the low outlet pressure. 5. Conclusions The present study uses the Bernoulli’s equation to analyze theoretically the whole flowing process in the ADS windowless spallation target and performs the numerical simulation for LBE liquid and vapour using the CFD simulation. In the theoretical analysis, the formulae for the height of the recirculation zone and the buffer zone are both acquired and can be used to guide the design or optimization of the target. In the numerical study, a novel method is put forward to calculate the height of the recirculation
Annex, I., 2005. EUROpean Research Programme for the TRANSmutation of High Level Nuclear Waste in an Accelerator Driven System, Project acronym: EUROTRANS, Contract no.: FI6W-CT-2004-516520. Batta, A., Class, A., 2007. Numerical investigations on geometrical designs of the windowless XT ADS spallation target. In: International Conference on Advances in Nuclear Power Plants (ICAPP 2007), Nice, France. Batta, A., Class, A., 2008. Free surface modeling and simulation of the water experiment for the XT ADS spallation target. In: Proceedings of the 2008 International Congress on Advances in Nuclear Power Plants. Anaheim, California. Bianchi, F., Ferri, R., Moreau, V., 2008. Thermo-hydraulic analysis of the windowless target system. Nucl. Eng. Des. 238, 2135–2145. Class, A.G., Angeli, D., Batta, A., Dierckx, M., Fellmoser, F., Moreau, V., Roelofs, F., Schuurmans, P., Van Tichelen, K., Wetzel, T., 2011. XT-ADS Windowless spallation target thermohydraulic design & experimental setup. J. Nucl. Mater. 415, 378–384. Du, G.S., 2007. Engineering Fluid Mechanics. China Electric Power Press. Harlow, F.H., Welch, J.E., 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225. Mcadams, W.H., 1954. Heat Transmission. McGraw-Hill Press. Roelofs, F., Siccama, N.B., Willemsen, S.M., 2007. Development of an Euler–Euler two-phase model for application in the windowless XT-ADS spallation target design. In: International Conference on Advances in Nuclear Power Plants (ICAPP 2007), Nice, France, p. 7092. Roelofs, F., Siccama, N.B., de Jager, B., van Tichelen, K., Dierckx, M., Heyse, J., Rosseel, K., Schuurmans, P., 2008a. Comparison of the hydraulics in concentric and three feeder XT-ADS windowless spallation target designs. In: Proceedings of ICAPP’08, Anaheim, USA, p. 8029. Roelofs, F., Siccama, N.B., Jeanmart, H., Tichelen, K.V., Dierckx, M., Schuurmans, P., 2008b. Application of a controlled swirl in the XT-ADS spallation target. In: International Conference on Advances in Nuclear Power Plants Anaheim, USA, p. 7029. Roelofs, F., de Jager, B., Class, A., Jeanmart, H., Schuurmans, P., Ciampichetti, A., Gerbeth, G., Stieglitz, R., Fazio, C., 2008c. European research on HLM thermalhydraulics for ADS applications. J. Nucl. Mater. 376, 401–404. Schuurmans, P., Guertin, A., Buhour, J.M., Cadiou, A., Dierckx, M., Heyse, J., Rosseel, K., Van Tichelen, K., Stieglitz, R., Coors, D., 2007. Design and R&D support of the XT-ADS spallation target. In: Utilisation and Reliability of High Power Proton Accelerators (HPPA5), p. 245. Sobolev, V., 2007. Thermophysical properties of lead and lead–bismuth eutectic. J. Nucl. Mater. 362, 235–247. Su, G.Y., Gu, H.Y., Cheng, X., 2012. Experimental and numerical studies on free surface flow of windowless target. Ann. Nucl. Energy 43, 142–149. Tichelen, K.V., Kupschus, P., Arien, B., Abderrahim, H.A., 2007. Design and verification experiments for the windowless spallation target of the ADS prototype MYRRHA. In: Nuclear Science Utilisation and Reliability of High Power Proton Accelerators: Workshop Proceedings, Mol, Belgium, p. 311–325. Tong, W., Chuang-ang, G., Bo, Y., Jian-de, H., 2003. PISO algorithm for unsteady flow field. J. Hydrodyn. 18, 233–239.