Influence of Micro Ribs Segment on Quasi-periodic Large-scale Vortex Structure in 4 Rod Bundle Lattices

Rod bundle lattices play a crucial role in nuclear reactors, steam generators, and heat exchangers. The inclusion of quasi-periodic large-scale vortex structures (QLVS) can enhance flow mixing between the channels of the rod bundle and improve the lattice’s heat transfer capability. To study the impact of micro-rib segments on flow and heat transfer in the lattice, the Reynolds stress model (RSM) is utilized. Results reveal that the arrangement of micro-ribs on the rod bundle surface promotes the generation of QLVSs. These micro-rib segments modify the flow field within the lattice, thereby influencing the QLVS. The drag coefficient and heat transfer coefficient of the rod bundle lattice with micro-rib segments show a positive correlation with the length of these segments compared with the standard rod bundle lattice.


Introduction
Since the 1950s, experimental studies have been conducted on the flow and heat transfer characteristics of rod-bundle cells, which have been widely used in engineering practice [1] .The quasi-periodic largescale vortex structure (QLVS) contributes significantly to mass, momentum, and energy exchange in the rod bundle lattice and can enhance flow mixing and heat transfer capability [2] .Researchers have conducted numerous experiments and numerical simulations on QLVS since its discovery [3] .Moller proposed a "vortex street" model that moves along the axial direction, while Kruss and Meyer measured various parameters of 37 rod bundle lattices, which suggested the existence of two rows of vortices with opposite rotation directions on both sides of the gap center [4] .QLVS originates from turbulence anisotropy and transverse velocity gradient between rod bundle lattices [5] , and a pitch-to-rod diameter (P/D) ratio of less than 1.1 is required for QLVS introduction in rod bundle lattices [6] .However, few studies have investigated QLVS introduction devices in rod bundle lattice, and this paper analyzes the influence of micro ribs on QLVS and lattice performance as a QLVS introduction method.

Geometry
Fig. 1 shows the vertical view of the micro ribbed rod bundle lattice.The shaded part is the flow channel.The length of the lattice is 1995 mm, rod diameter (D) is 20 mm, and P/D=1.25.The side length (e) is 1.5 mm, and the distance from the rod axis to the wall (W/2) is 12.5 mm, the circumferential interval is 10°, and the axial spacing is 15 mm.Fig. 2 shows the geometric model and observation positions.3 shows the distribution of the micro ribs segments of the six kinds of lattices.The shaded area is the micro ribs segment which is the rod bundle lattice segment with micro ribs, and the white area is the standard segment.

Turbulence model and boundary conditions
The Reynolds Stress Model (RSM) is a turbulence model that considers anisotropy and is well-suited for simulating large-scale turbulence [7] .After verifying its applicability and ensuring grid independence [5] , the RSM is used to numerically simulate rod bundle lattices with 6, 830, 880 grids.Water is used as the flowing medium, with an inlet velocity of 4.5 m/s, an inlet temperature of 10 ℃, and an inlet pressure of 101325 Pa.The rod bundle surface is subjected to a constant heat flux of 202, 488 W/m 2 .The numerical calculation employs a transient method with an adaptive time step.

Influence of physical parameters
The physical parameters of fluid are important parameters affecting the heat transfer of lattices.The influence of physical parameters within the calculation range on the calculation results is analyzed.The geometric structure of rod bundle lattices is shown in Fig. 3 The density of water is denoted by ρ in units of kg/m 3 , while μ represents the dynamic viscosity coefficient in units of kg/(m•s).The thermal conductivity is represented by γ in units of W/(m•℃), and c p denotes the specific heat at constant pressure in units of kJ/(kg•℃).The Q factor criterion is used to evaluate the strength of QLVS [8] .Fig. 4 illustrates the Q factor contours at Plane 1 and Plane 2, with the white shadow indicating the projection of the micro ribbed bundles on the observation plane.It is observed that the strength of QLVS in Case 2 is lower than that in Case 1 at the rod-rod gap and rodwall gap.Table 1 shows the normalized drag coefficients (λ f /λ a ) and the normalized Nusselt number (Nu f /Nu a ) in the micro-ribbed rod bundle lattices.The deviations are 1.2% and 0.5%, respectively, where a and f are different rod bundles in Fig. 3

QLVS
The development of flow fields within each lattice is presented in Fig. 5.As the flowing medium enters the lattices, the flow fields are redistributed.Within the micro ribs segment, the velocity of water in the central channel increases, while the velocity of water at the rod-rod and rod-wall gaps decreases.Once QLVS is generated, the velocity of water at the rod-rod gap and rod-wall gap increases.

Fig. 5. Development of flow field within each lattice
The lateral velocity fluctuation characterizes the strength of QLVS to some extent.Fig. 6 shows the lateral velocity fluctuation at the rod-rod gaps of each lattice.Lattice b has a lateral velocity fluctuation amplitude of less than 2%, which is regular in the micro ribs segment.From both Fig. 5(a) and Fig. 7(a), it is evident that the flow field redistribution in the micro-rib section has already been accomplished, and QLVS has not been generated yet.This suggests that QLVS needs a certain length to develop.From the calculation results of lattices c, d, and e, it can be seen that QLVS is introduced at about 1 m of the micro ribs segment.The micro ribs segment of lattice c is arranged after the redistribution of the flow field, which has little effect on the early introduction of QLVS.Compared with lattice d, lattice e has micro ribs segment arranged at intervals after QLVS is generated, which slows down the attenuation of QLVS.

Redistribution of the flow field
The flow fields of lattices a, c, and f are analyzed to determine the influence of the flow field on QLVS.Fig. 8 shows the change of flow field within each lattice.After the flow field redistribution, the flow field of lattice a tends to be stable after 0.8 m, the flow field of lattice c tends to be stable after 1 m, and the flow field of lattice f tends to be stable after 0.5 m.The use of micro ribs segments reduces the length required for flow field redistribution.This means that the velocity of water in the center channel changes less, and the velocity of water at the rod-rod and rod-wall gaps is decreased by 26.0% and 27.4%, respectively.Fig. 8. Redistribution of the flow field Fig. 9 illustrates the lateral velocity fluctuations at the rod-rod gap and rod-wall gap in lattices c and f.It can be seen that QLVS is gradually generated after the flow field is fully developed.This indicates that the generation of QLVS requires a certain velocity gradient at the rod bundle gap.After 1.605 m of the standard segment in lattice c, the lateral velocity fluctuation gradually attenuates.This is due to the gradual decrease of the velocity gradient at the rod bundle gap.  2 shows the normalized drag coefficients (λ/λ a ) and Nu/Nu a of each lattice, where λ a is the drag coefficient and the Nusselt number of the standard rod bundle lattice is denoted as Nu a .Compared with lattice a, the drag coefficient and Nu of other lattices increase, the increased multiple of drag coefficient is linearly related to the length of the micro ribs segment, and the increased multiple of Nu is positively related to the length of the ribs segment.The drag coefficient and Nu of lattice f increased by 94.9% and 20.4%, respectively.

Conclusions
(1) The QLVS in the standard section behind the micro ribs section gradually attenuates, and the placement of the micro ribs segment at this interval can better maintain the QLVS.
(2) After the redistribution of the flow field is completed, the arrangement of the micro ribs segment does not promote the early introduction of QLVS.
(3) Arranging micro-ribs in rod bundles can introduce QLVS, which requires a certain length and velocity gradient.
(4) The length of the micro ribs segment has a positive correlation with the drag coefficient and Nu of the rod bundle lattice with the micro ribs segment when compared with the standard rod bundle lattice.

Fig. 6 .
Fig.6.Lateral velocity fluctuations at rod-rod gaps Fig.7shows the lateral velocity fluctuation at the rod-wall gaps of each lattice.Lattice b exhibits a lateral velocity fluctuation with an amplitude of less than 2%, indicating that QLVS is not introduced.On the other hand, lattices c, d, and e exhibit QLVS with a lateral velocity fluctuation amplitude of approximately 19% and a wavelength of approximately 31.9 mm.After the micro ribs segment, the lateral velocity fluctuation of QLVS gradually attenuates.After two wavelengths, its amplitude decreases by 18% and the wavelength increases by 9%.QLVS is well maintained due to the micro ribs segment arranged in the interval of lattice e.

Fig. 9 .
Fig. 9. Lateral velocity fluctuations3.3.Drag coefficient and Nusselt numberTable2shows the normalized drag coefficients (λ/λ a ) and Nu/Nu a of each lattice, where λ a is the drag coefficient and the Nusselt number of the standard rod bundle lattice is denoted as Nu a .Compared with lattice a, the drag coefficient and Nu of other lattices increase, the increased multiple of drag coefficient is linearly related to the length of the micro ribs segment, and the increased multiple of Nu is positively related to the length of the ribs segment.The drag coefficient and Nu of lattice f increased by 94.9% and 20.4%, respectively.

Table 1 .
. Normalized drag coefficient and Nusselt number λ f /λ a Nu f /Nu a According to the calculation results, the flowing medium whose physical parameters vary with temperature is used.

Table 2 .
Normalized drag coefficient and Nu