1. Introduction

The Chinese Academy of Sciences (CAS) has launched an engineering program for nuclear transmutation by developing an accelerator driven subcritical (ADS) system. The design proposed by the Institute of Nuclear Energy Safety Technology (INEST), was selected as the reference reactor ^{[1][2][3][4][5]}. Initially, the design of a 10 MW_th lead-bismuth cooled research reactor was under consideration ^{[6][7][8][9][10]}. The ADS system is an advanced stage nuclear energy system for the transmutation of long-lived radioactive waste and fission fuel breeding ^{[8][9][10][11][12][13][14]}.

Nuclear fuel is the most critical and important component that bears safety Class-III, ASME Class-I, and seismic Class-I code components. To accomplish the requirements laid down in the codes, seismic qualification of the fuel rod is mandatory with respect to operational basis earthquakes (OBEs) and safe shutdown earthquakes (SSEs). Researchers have studied the potential failures of fuel rod cladding and have shown that the mechanical failure of fuel rods encompasses cladding collapse, fatigue fracture, and rupture, and that these excessive stresses on cladding are usually caused by different operational transients during the lifetime of a plant ^[15]. The authors proposed the RODSIS rod design model, whereby the fuel rods were fastened using a stiff middle-grid and softer end-grids that were made of HT-9 due to high coolant density. Finite element analysis (FEA) was conducted using ANSYS for thermal and mechanical analyses of the middle grid only, and validated that for a peak power of the fuel rod, adequate margins exist against static stresses, fuel melting, clad oxidation, and fuel cladding chemical interaction (FCCI) without taking into consideration the seismic aspect. Another study highlighted the mechanical response, deformation, and bowing of wire-wrapped fuel rods and their effect on the wrapper by considering their neutronic and thermal environments for liquid metal fast breeder reactor (LMFBR) fuel assembly ^[16][17][18]. A sub-channel deformation analysis code (SHADOW) for wire-wrapped fuel assemblies was developed and applied to study the deformation due to thermal bowing of 169 fuel pins of a prototype fuel assembly of an LMFBR. This code was considered to be an effective tool for thermal and structural analysis of fuel assembly, but it lacks the capability to accommodate dynamic effects in the event of an earthquake event. The flow path of the coolant between the rods within the fuel assembly is maintained either by tightly wrapped thin wires around the rods or by grid spacers. The Fermi reactor in the U.S. and the demonstration and prototype plants in Germany and the U.K. used grid spacers, whereas a wire-wrapped design has been adopted for the fuel assembly design by other plants ^[19][20], which focused on the computational fluid dynamics (CFD) analysis of a 19-pin, wire-wrapped, LBE cooled fuel assembly of a GEN-IV research reactor. A CFD and sensitivity analysis model was developed to describe and validate the experimental test section ^[20]. This code was validated by the experimental data of a similar geometry cooled by sodium by considering only the heat transfer effects.

A steel wire of a usually circular cross-section is welded to the extreme ends of cladding and wrapped around the cladding with a quantified axial pitch. The formerly used grid-spacer design usually consists of a steel web-like structure containing rods, which is attached to the fuel assembly duct wall at designated axial levels depending upon the length of the assembly. Wire-wrapped designs are widely preferred for their several benefits, including that fabrication is easy and less expensive when compared to the grid-spacer design that was usually employed in the previous generation of reactors ^[20]. Due to the use of wire-wrapped technology, contact with neighboring cladding occurs at six axial locations for every pitch of wire, which helps to minimize cladding mechanical vibrations. The grid design requires several grids to provide a similar structural stability, thus resulting in an unnecessary pressure drop. On the other hand, the added advantage of the wire-wrapped design is that it enables a better heat mixing of the coolant due to an increase in the local turbulence of the coolant.

Generally speaking, mostly of the studies that have been conducted so far in the research and development of LMFRs relate to heat transfer and fluid dynamics. To some extent, literature exists regarding the justification of the seismic design of reactor components as a whole (fuel assembly or core), but is limited to individual fuel rods or a comparison between different designs of fuel rods. The present study highlights the comparison of two different designs of fuel rods that are under consideration for the CLEAR-I (China Lead-Based Research Reactor) and presents their qualification in detail by considering different loads (e.g., dead weight (DW)), design and operating pressures (DP, OP), earthquakes (as response spectrum), different plant conditions, and combinations of the aforesaid loads according to code requirements using ANSYS mechanical APDL code (ANSYS parametric design language). The present work deals with the seismic and stress analyses of the Class-I component that should be confirmed "by analysis" instead of "by rules" ^[21][22].

2. Structural Design and Modeling

The fuel rod comprised a 15-15Ti stainless-steel cladding holding UO₂ pellets ^[23] enclosed by upper and lower end caps, along with reflectors, gas chambers, and a ballast for compensating the buoyancy caused by the high density of the LBE. Based on the CLEAR-I design, each fuel assembly consisted of 61 fuel rods ^[24][25]. The two designs under consideration differed in geometry in terms of one having a tightly wrapped wire around cladding and being welded at extreme ends of the cladding. The remaining features of the two designs are completely identical. Figure 1 shows the schematic of two different fuel rod designs for the CLEAR-I.

Fig. 1Full-screen View

(Color online) Schematic views of two different designs of the CLEAR-I. (a) Schematic view of the wire-wrapped fuel rod (b) Schematic view of the bare design

The fuel rods in most LMFR’s assemblies are separated by wire that is usually of a very small diameter, which is wrapped helically around the fuel-rod cladding (wire spacers) along its axis. These wire-wrapped fuel rods were initially designed to maintain a constant gap among the fuel rods, but it was later found that they also provide additional turbulence and cause rotation of the liquid metal coolant within the assembly as it flows through the core ^[26]. In consideration of the service conditions and design load cases, the preliminary structural design parameters and material properties of fuel rods are listed in Tables 1 and 2.

During assembling, the pellets are piled within the cladding to the required height. A compressive spring is then installed on the top of the fuel column, and the upper and lower end plugs are inserted and welded onto the ends of the clad tube. In order to minimize clad stresses and clad flattening due to the coolant operating pressure, the fuel rod is internally pressurized with helium during the plug welding process. An initial rod pressure is selected to slow down the pellet-clad mechanical interaction and to avoid the probability of rod flattening.

Modeling of the wire around cladding requires special care and attention because the wire should remain in contact with the cladding along the whole length of the cladding. Wire surrounds the cladding in complete full 03 loops or turns. By choosing a correct angle and performing orientation calculations for modeling, the ANSYS model is able to attain the geometry that is closest to the actual geometry. The cladding was divided into equal numbers after exact calculations of wire turns and radius were performed. A helical path was made around the rod centerline according to the number of cladding divisions. A circular cross-section equal to the wire diameter was created for the wire, which was away from and exactly equal to the radius of wire, on the bottom horizontal plane. This was then simplified radially to reduce the cell count followed by sweeping the cross-section along the helical path. The purpose of the geometric estimation in this method is to keep the wire perfectly horizontal instead of normal to the helical path in order to resemble the real geometry because of the selection of the sweep path and the orientation of the plane on which the sweep sketch was made. By using accurate wire dimensions, this problem is hardly evident: the angle between the wire normal plane and the horizontal plane is smaller, so the variation in the sweep is considerably small and can therefore be ignored ^[27]. ANSYS 3-D models of both designs and wire are shown in Fig. 2.

Fig. 2Full-screen View

(Color online) Three-dimensional models of fuel rods and wire. (a) 3-D model of the wire-wrapped design; (b) 3-D model of the wire; (c) 3-D model of the bare design

3. Methodology of Analysis and Assumptions

DP (0.9 and 3.75 MPa) and OP (0.6 and 2.5 MPa) were applied on the outside and inside areas of the cladding. Only plant operating conditions that involve seismic loadings were considered. Thus, the service levels with a loading combination other than seismic loads were overlooked, as listed in Table 3. Moreover, in the absence of nozzles, service levels B and C are the same.

3.1 Floor Response Spectrum

The U.S. NRC RG 1.60 spectra was used as the site response spectrum. The design response spectra for SSEs was characterized by RG 1.60 spectra, the horizontal component of which was scaled to a maximum ground acceleration of 0.3 g and the vertical component was scaled to a maximum ground acceleration of 0.217 g, which are considered to be fit for a typical site in China for an LMFR. The response spectra for horizontal and vertical components of OBEs were obtained by dividing the corresponding values of the SSE spectra by 2. Figure 3 shows the acceleration versus frequency curves for OBEs and SSEs. The spectrum amplification factors for SSEs and OBEs are all in accord with RG 1.60.

Fig. 3Full-screen View

(Color online) Horizontal and vertical response spectrums for OBEs and SSEs (a) Horizontal and vertical response spectrum for OBEs; (b) Horizontal and vertical response spectrum for SSEs

Since the fuel rods first-order natural frequencies (Table 4) are 8.07 Hz (bare) and 7.91 Hz (wire-wrapped), they are less than the zero-period acceleration of 33 Hz; hence, the seismic calculation of the equivalent static method could not be applied. The FEM based software ANSYS was used in this analysis. The methodology is presented in a flow chart in Fig. 4.

Fig. 4Full-screen View

Methodology of analysis

Table 4Full-screen View

Mesh details

Model type	Element type	Total elements	Total nodes
Bare	Solid95	658,560	1320976
Wire-wrapped	Solid95	1178846	2282429
	Targe170
	Contac174

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Following assumptions were made before undergoing any analysis:

The fluid (LBE) was viscous, incompressible, stationary and Newtonian gravity effects were neglected. The rod bundle did not undergo any deformation, and the pitch between the rods remained constant in the fuel assembly. The effective density method was used for the analysis, which included the density of all integral components of the fuel rod to form a cumulative mass for the fuel rod. In a stationary fluid, added stiffness is typically quite small compared to the structural stiffness, and can therefore be ignored. The model was then investigated by static (pressure and weight) and dynamic (OBE and SSE) analyses, whereby loads were applied and results were compared with the allowable limits defined by code.

3.2 Mesh Detail and Mesh independency study

After modeling in 3-D with the necessary details, the models were discretized with a higher-order 20-node 3-D solid element (SOLID95) to tolerate irregular configurations of geometry without loss of certainty. SOLID95 is compatible with displacement shapes and is appropriate for curved borders ^[28]. The type of elements used and the total number of elements and nodes used in this analysis are listed in Table 4, and the 3-D meshed view of the fuel rod and the wire are shown in Fig. 5.

Fig. 5Full-screen View

(Color online) Meshed models of the fuel rod and wire. (a) Meshed model of the wire-wrapped design; (b) Meshed model of the wire.

The authenticity of the FEM results is based upon the convergence of solution, i.e., the results should become independent to the mesh or grid size. The grid independency procedure provides the basis for selecting the optimum mesh-size for better and accurate results with minimal processing time. The meshed fuel rods (bare and wire-wrapped) were subjected to a calculated stress with three different meshed states:

(i) A coarse mesh of (0.262075, bare) and (1.923422, wire-wrapped) million total nodes;

(ii) A medium mesh of (1.320976, bare) and (2.282429, wire-wrapped) million total nodes;

(iii) A fine mesh of (1.51195, bare) and (3.311429, wire-wrapped) million total nodes.

The analysis results revealed that the solution became independent to the mesh size for both models when the total number of nodes were (1.320976, bare) and (2.282429, wire-wrapped) million, as can be seen in Fig. 6, which plots the average stress intensity (S_INT) against the number of nodes.

Fig. 6Full-screen View

Mesh dependency. (a) Bare; (b) Wire-wrapped.

4. Contact Analysis Strategy for Wire-wrapped Design

ANSYS FEA has a huge library of elements. These elements range from those that are simple, complex, sophisticated, and of general purpose. Selection of the best choice of contact element and solution options can greatly affect the results and system performance. By considering the geometry of the cladding and by keeping in view the layout of the wire-wrapped around the cladding, surface-to-surface contact elements TARGE170 and CONTA174 are best suited to this analysis because they overcome most of the restrictions or limitations of other elements. This is due to the fact that 3-D systems with rigid or flexible target faces can be treated, sliding is permitted, higher-order solid (e.g., Solid95) element faces are compatible, and stiffness can be assigned automatically for a closed gap. The software assigns default values of parameters for contact elements but still provides the user with a selection of different options: stiffness of a closed gap (FKN), formulation methods (penalty method or penalty plus LaGrange multipliers), allowable penetration tolerance (FTOLN), pinball region size (PINB), friction/sliding behavior, and initial closure (ICONT). For this analysis the default values assigned by the software were used.

4.1 ASYMMETRIC Pattern of CONTACT Elements

Asymmetric contact pattern defines the selection of target and contact surfaces and assigns all the contact elements on a contact surface and the target elements on a target surface. This is also called 'one pass contact’ and is the most efficient way of modeling surface-to-surface contact. ANSYS provides the following guidelines for defining the contact and target surfaces in a model for TARGE170/CONTA174 elements: If convex and flat or concave surfaces come into contact, the concave/flat surface would be the target surface. If fine and coarse mesh surfaces come into contact, the coarse mesh would be the target surface. If stiffer and softer surfaces come into contact, the stiffer surface would be the target surface. If surfaces with higher and lower order elements come into contact, the lower order element surface would be the target surface. The general layout for surface-to-surface contact is shown in Fig. 7.

Fig. 7Full-screen View

(Color online) General layout of surface-to-surface contact

Keeping in view the aforementioned guidelines, the wire-wrapped around the cladding was treated as the target surface because the solid wire of 1.6 mm diameter was much stiffer and the cladding was treated as the contact surface in this analysis. The cladding surface was meshed with CONTA174 and the wrapped wire surface was meshed with TARGE170 elements. While using the TARGE170/CONTA174 element pair meshing, the following elements from the KEYOPT and SOLUTION settings were considered after a detailed review of available literature and the ANSYS guidelines to expedite the solution: KEYOPT,3,2,1, KEYOPT,3,6,0, KEYOPT,3,7,0, KEYOPT,3,8,1, KEYOPT,3,9,1, KEYOPT,3,11,0, KEYOPT,n,12,5; SOLCON, OFF, OFF, NSUBST, 1, 1, 1, NEQIT, 1, LNSRCH, OFF, NLGEOM, OFF.

"Always bonded" contact was found to be a very useful feature. The use of contact elements is quite ideal when compared to the constraint equations to connect different meshes because the contact elements function is appropriate for large deformation problems, whereas the constraint equations are limited to small deformations.

5. Results and Discussion

Since fuel pellets are not a solitary integral piece, they do not contribute during the bending moment. The fuel column was therefore divided into small pieces (pellets), which did not defy the bending of the fuel rod ^[26][27]; hence, it can be fairly assumed that the pellets contributed only to the mass of the fuel rod and not to the stiffness, and that the mass per unit length collectively included the fuel and cladding ^[28]. The lower end cap was constrained in all degree of freedom (DOF), whereas the upper-end cap was constrained in horizontal directions, thereby allowing room for thermal expansion of the fuel rod in the vertical direction.

5.1 Modal Analysis in A Vacuum and in LBE

Modal analysis of the two designs was compared in a vacuum and in LBE by means of potential flow theory using the added mass effect (i.e., the mass of LBE displaced by the fuel rod volume). The added mass effect in the system due to LBE (higher density in comparison to the vacuum), was inversely proportional to the natural frequencies. The results obtained from the modal analysis showed very little difference in natural frequencies and mode shapes of the two designs. The wire-wrapped design showed a small lag in both mode shapes and natural frequencies in comparison to the bare design because of an increase in mass, as exhibited in Fig. 8.

Fig. 8Full-screen View

(Color online) Mode shapes comparison of the two designs in LBE. (a) Bare; (b) Wire-wrapped.

Referring to recent numerical studies, the hydrodynamic function (τ) for a circular cylinder and a thin rectangular beam are approximately identical. Furthermore, it has been reported that the hydrodynamic functions for a rectangular beam and a circular cylinder possess the same asymptotic forms, and the difference in the results never exceeds 15% over the entire frequency range ^[29].

${\text{ω}}_{\text{lbe}}{}_{\left(n\right)}={\text{ω}}_{{\text{vac}}_{\left(n\right)}} {\left[\left(1+\frac{\pi l{\rho }_{\text{lbe}}}{4t{\rho }_{\text{rod}}}\right){\tau }_{\left(n\right)}\right]}^{-1/2}$ …(1)

where, ${\text{ω}}_{\text{lbe}}$ and ${\text{ω}}_{\text{vac}}$ are frequencies in LBE and the vacuum, ${\rho }_{\text{lbe}}$ and ${\rho }_{\text{rod}}$ are densities of LBE and the rod, and $l$ and $t$ are the length and thickness of the fuel rod. Substituting values gives a constant hydrodynamic function (τ) over the entire frequency range, which further validates the FEM modal analysis results. The vacuum and LBE frequency comparison results for the verification of the hydrodynamic function are listed in Table 5.

Table 5Full-screen View

Natural frequency comparison of two designs in a vacuum and in LBE and hydrodynamic function verification

Medium	Design	Mode		1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
Vacuum	Bare	Frequency (Hz)		8.07	8.27	22.2	22.76	43.44	44.53	71.63	73.44	106.73	109.43
	Wire-wrapped	Frequency (Hz)		7.91	8.35	21.53	22.09	42.01	42.93	69.45	71.03	103.99	106.57
LBE	Bare	Frequency (Hz)		7.57	7.76	20.84	21.36	40.77	41.79	67.23	68.93	100.18	102.71
	Wire-wrapped	Frequency (Hz)		7.38	7.78	20.07	20.6	39.17	40.02	64.75	66.23	96.95	99.36
Hydrodynamic function (τ)			Bare	9e-4	9e-4	9e-4	9e-4	9e-4	9e-4	9e-4	9e-4	9e-4	9e-4
Hydrodynamic function (τ)			Wire-wrapped	1e-3	1e-3	1e-3	1e-3	1e-3	1e-3	1e-3	1e-3	1e-3	1e-3

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5.3 Stress Distribution and Evaluation of Results

The maximum stressed nodes, as sorted for ease of understanding the results, provide a comparison for the two different designs of LMFR fuel rods for different plant conditions. The stress distribution or stress contours has been compared along the most stressed nodes of the fuel rods at different loading conditions. As shown in Fig. 9, the most stressed nodes for the bare design are at the joint of the cladding with the end caps or cladding plugs, whereas they are at the extreme welding ends for the wire-wrapped design due to the discontinuity in geometry (i.e., the connection of the wire with the cladding). The contours were elaborated in terms of stress intensity (i.e., twice the maximum shear stress), which was defined as the difference between the algebraically largest and smallest principal stresses at a given position. To evaluate the results, the calculated stresses were compared with the allowable stress limits defined by the code, which showed that they were within the allowable limits.

Fig. 9Full-screen View

(Color online) Stress intensity contour comparison of two designs for different plant conditions. (a) Design condition (Bare) (b) Faulted condition (Bare) (c) Design condition (wire-wrapped) (d) Faulted condition (wire-wrapped)

Stress classification was performed to identify the "primary" (P) and "secondary" (Q) stresses. Primary stresses relate to equilibrium equations, while secondary stresses are linked to compatibility equations. In general, these stresses come from mechanical and thermal loadings, respectively. The integrity of the cladding is of the main concern of this study because it is the thinnest and longest section and bears all the mechanical loads. In the FEM, when continuum elements are used, the total stress distribution is obtained. Therefore, to calculate the membrane (P_m) and bending stresses (P_b), the stress distribution should be linearized across the thickness ^[26]. To check the stress limits and gain a better understanding of the behavior of the cladding for the two different designs, paths were defined along the full length of the cladding. The selection of the same path distance was considered for both models in order to get a true picture of the results. The stresses were then linearized and compared with the allowable limits[32]. For ease in understanding and for simplification, only four paths (the lowest and uppermost, and middle two paths of cladding) were selected and the ratio was also determined between calculated and allowable stress, for P_m + P_b whichever is maximum (inside, center and outside of the cladding), listed in Table 7.

Table 7Full-screen View

Stress evaluation comparison of fuel rod cladding under different plant conditions

Service level/ Allowable stress	Distance (mm)		Bare				Wire-wrapped
		Path	Calculated stress (MPa)			Ratio	Calculated stress (MPa)			Ratio
			Pm+Pb				Pm+Pb
			Inside	Center	Outside		Inside	Center	Outside
Design (1.5Sm = 180)	0	1	1.39	1.33	1.27	0.008	79.16	106.4	133.8	0.74
	510	7	38.8	41.45	44.3	0.25	39.94	41.36	44.19	0.24
	1105	14	38.69	41.44	44.29	0.25	38.88	41.36	43.98	0.24
	1630	20	22.76	15.55	10.51	0.13	13.1	8.4	7.49	0.07
Normal (3Sm = 360)	0	1	0.81	0.77	0.74	0.002	69.02	97.14	125.5	0.35
	510	7	26.07	27.63	29.54	0.08	27.39	28.29	29.46	0.08
	1105	14	25.82	27.63	29.53	0.08	25.94	27.57	29.33	0.08
	1630	20	15.21	10.41	7.01	0.04	8.42	5.61	4.67	0.02
Upset (3Sm = 360)	0	1	2.8	2.69	2.59	0.008	104.5	103.9	115.2	0.32
	510	7	25.77	27.63	29.53	0.08	25.69	27.57	29.46	0.08
	1105	14	25.74	27.63	29.52	0.08	25.85	27.57	29.32	0.08
	1630	20	9.04	4.83	7.22	0.02	17.81	23.56	30.57	0.08
Faulted (3.6Sm = 432)	0	1	1.96	1.95	1.93	0.004	71.34	101.5	132.1	0.3
	510	7	26.08	27.63	29.54	0.07	27.03	27.93	29.46	0.06
	1105	14	25.82	27.63	29.53	0.07	25.91	27.57	29.32	0.06
	1630	20	15.22	10.44	7.02	0.03	13.23	11.34	10.47	0.03

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A graphical comparison was prepared to provide a better understanding of the two designs for different plant conditions (Fig. 10). Twenty paths were selected on the full length of the cladding by bearing in mind the same path distance for the two models in order to make a clear and true comparison between the two designs. It is interesting to note that the behavior of the two models for different plant conditions were opposite to each other at the beginning of the cladding length (0 mm distance) because of the discontinuity in geometry due to the attached wire. In structural discontinuity, there is an obvious increase in stress that can be observed due to the compatibility between linking parts. For the remaining length of the cladding, both models behaved in almost the same way for different loading combinations. The stresses remained uniform throughout the cladding length except for a small difference between the two models at the top section of the cladding (Fig. 10).

Fig. 10Full-screen View

(Color online) Stress distribution comparison of two designs along the cladding length for design and faulted conditions. (a) Design condition; (b) Operation condition; (c) Upset condition; (d) Faulted condition

6. Analytical Solution for Static Pressure

The prime concern in relation to the fuel rod is cladding. For the static analytical solution, the cladding can be treated as a thin cylinder since it satisfies the following laws of thin and thick cylinders:

od > 10t or id/t > 20,

where od is outside diameter, t is thickness, and id is the inside diameter of the cladding. When r_o = 6 mm, t = 0.4 mm, and id = 11.6 mm, the criteria that the cladding could be treated as a thin cylinder are satisfied.

The method for determining the hoop or tangential stresses (δ_t), which are considered to be uniform throughout the wall thickness, and the radial stresses (δ_r), which are insignificant in comparison to the hoop stress, at any thickness of a cylinder against the applied pressure was presented by the French electrician Gabriel Lame in (1833). This applies to a cylinder with a given inside radius (r_i) and outside radius (r_o) subjected to a uniformly distributed internal (P_i) and external pressure (P_o) [33].

When considering a thin shell of the radius (r) for the thickness (dr), the tangential stress in this shell is δ_t, the radial stress on the inner surface is δ_r, and that on the outer surface is δ_r + dδ_r, where dδ_r is the increment in δ_r due to the variation of pressure across the cylinder wall. The radial stresses are assumed to be tensile, so a negative result for δ_r will denote compression. Hence, for equilibrium; the vertical summation of forces must be zero:

The final equation obtained from solving Eq. (9) gives the following general expression for δ_t and δ_r at any point:

Substituting values for all variables and different values for 'r’ against the design and operating pressures in Eq. (10), we obtain the following results in comparison to the ANSYS calculations (Table 8). The results were roughly compared with the ANSYS exact calculations and the two showed a close agreement.

It should be mentioned that for thin-walled cylinders, radial stresses are usually neglected because they are negligibly small. Due to internal pressure, the deformation of the cladding takes place, which results in stresses in the cladding wall. Each wall element is subjected to circular and axial expansion and radial compression that is governed by Eqs. (12) and (13). The inside wall deformation at r = r_i is given as:

The outside wall deformation at r = r_o is expressed as:

By substituting values into Eqs. (12) and (13) we obtain an estimated inside wall deformation $\Delta r_i=0.00157 \text{mm}$ and an outside wall deformation $\text{Δ}{r}_{\text{o}}= 0.00135 \text{mm}$.

7. Conclusion

A comparison of two different designs of lead-based reactor fuel rods was established for different plant conditions. ANSYS contact analysis methodology was developed for the wire-wrapped design and most appropriate KEYOPT and SOLUTION settings were suggested. A simple yet accurate method for the determination and verification of the added mass effect was presented and verified using a manually calculation to show the usefulness of the potential flow theory for simple geometries. Modal frequencies were compared in a vacuum and in LBE, and a constant hydrodynamic function (τ) validated the FEM results. The use of wrapped-wire provided thermal mixing of the coolant due to increased local turbulence in the coolant flow, although this resulted in high-stress ratios on the extreme welded locations of the cladding. In comparison to the bare design, the wrapped-wire design yielded better stress results but with some compromise in other aspects. Wire-wrapped designs are widely preferred due to several benefits including the fact that fabrication is easy and less expensive when compared to the grid-spacer design that was usually employed in the previous generation of reactors. Secondly, due to the use of wire-wrapped technology, the contact with neighboring cladding occurred at six axial locations for every pitch of wire, which helped to minimize cladding mechanical vibrations and reactivity oscillations. Furthermore, the results were verified numerically and provided a close approximation to the ANSYS results. A mesh dependency test was also performed to determine the accuracy of the meshed model and to further validate the use of the APDL code for LMFR fuel rods analysis. The stresses remained uniform throughout the cladding length with a small difference at the top section of the cladding. The maximum stress ratios of 0.25 (bare) and 0.74 (wire-wrapped) that were computed on the cladding of the fuel rods in terms of the design condition were within the allowable limits defined by code. Hence, it is concluded that both fuel rod designs are adequate to bear the anticipated loads and will perform functions in all plant conditions. These results provide detailed insight for the design of LMFR fuel rods in consideration of different technical aspects and provide guidelines for further analysis.