In blind football, players predict the sound location of a ball to underpin the success of ball trapping. It is currently unknown whether blind footballers use head movements as a strategy for trapping a moving ball. This study investigated characteristics of head rotations in blind footballers during ball trapping compared to sighted nonathletes. Participants performed trapping an approaching ball using their right foot. Head and trunk rotation angles in the sagittal plane, and head rotation angles in the horizontal plane were measured during ball trapping. The blind footballers showed a larger downward head rotation angle, as well as higher performance at the time of ball trapping than did the sighted nonathletes. However, no significant differences between the groups were found with regards to the horizontal head rotation angle and the downward trunk rotation angle. The blind footballers consistently showed a larger relative angle of downward head rotation from an early time point after ball launching to the moment of ball trapping. These results suggest that blind footballers couple downward head rotation with the movement of an approaching ball, to ensure that the ball is kept in a consistent egocentric direction relative to the head throughout ball trapping. In ball trapping, players need to predict the trajectory of the upcoming ball and intercept the ball corresponding to the position. Therefore, accurate localization of the ball using auditory information is necessary to underpin the success of ball trapping.Blind football is designed to enable blind and partially sighted individuals to take part in the sport. Players localize the positions of the ball, teammates, and opponents by listening to sounds during games and daily training. The ball contains a sound system that causes it to make a noise when it bounces and rolls2. For example, blind footballers are more precise than blind and sighted individuals in identifying the direction of sounds emitted from static loudspeakers4. Velten et al. also reported that blind footballers showed less-frequent front–back confusion4—that is, when a stimulus in front of a subject is localized to the rear, or vice versa5—which occurs due to the so-called “cone of confusion”7. A more recent study by Mieda et al.8 revealed that blind footballers had faster choice reaction times, but not simple reaction times, compared to sighted footballers when executing a stepping response towards the perceived direction of the static loudspeakers. They suggest that blind footballers identify sound direction more rapidly based on auditory cues, while also maintaining accuracy, compared to sighted footballers and nonathletes. Based on these findings, it is reasonable to assume that rapid and accurate identification of sound direction with auditory cues represents a strategy of blind footballers. However, to our knowledge, there has been no study on the strategy of blind footballers to identify the direction of a dynamic sound source, such as a moving ball, which is necessary to perform ball trapping.Previous studies have indicated that blind footballers accurately localize sound direction using auditory cues that humans are known to benefit from when localizing a sound11, and improve accuracy of sound localization in the horizontal12 and elevation14 planes. The effect of head movements on sound localization has been studied previously by identifying the direction of the static sound source. Even in the case of localizing moving sound sources, some studies15 have reported that head movements also improve the accuracy of sound localization  when listeners moved their head while audio signals were moved, compared to when listeners remained still during the audio signal motion. Taken together, head movements appear to be important in ball trapping, which requires the accurate identification of the direction of a dynamic sound source . Here, we investigate whether blind footballers use horizontal and vertical head movements to underpin the success of ball trapping.Two aspects are important to increase the accuracy of sound localization. The first is to move the head; it is well known that head movements increase the accuracy of sound localization  when listeners are allowed to move their head during sound presentation. Previous studies have reported that head movements can reduce front–back confusion16. Previous studies have reported that sound localization is particularly accurate when the sound is in front of the listeners’ heads19. For instance, Makous & Middlebrooks19 showed that the size of errors and response variability were smallest for sounds presented in front of the listeners’ heads, while they were increased when the sounds were presented at more peripheral stimulus locations. Therefore, it is important for sound to be localized in front of the head using head rotation when localizing sounds from peripheral locations.The second aspect is to direct the head towards the sound source, which is necessary for accurate localization20. Furthermore, higher accuracy of pointing to auditory targets was observed under the condition in which listeners showed a larger heading angle to the targets, as well as with a larger amplitude of head movements21. The authors suggest that the accuracy of pointing to auditory stimuli could be due to the contribution of heading towards the target providing a more accurate frame of reference for the anticipated control of pointing. Collectively, it is predicted that the direction of the auditory stimulus relative to the position of the head could affect the performance of auditory–motor tasks in blind footballers.Auditory–motor performance, such as reaching and pointing to auditory targets, is also influenced by the location of a sound source in relation to the listeners’ heads. For instance, pointing error to auditory targets has been found to be smaller at the height of the chest than at the height of the feet22 and baseball25, skilled batters have been shown to couple their head direction to the movement of the ball, known as a “head-ball coupling” strategy, in order to track the target. For instance, elite batters demonstrated a head-ball coupling movement when the ball direction was kept in a constant direction corresponding to the head in real batting25. Crucially, Mann et al.22 indicated an advantage to keep the target in a consistent direction relative to the head, because visuo–motor tasks, such as catching and hitting, are controlled in an egocentric manner. Based on the previous findings showing that sound location was mainly coded in head-centred reference frame27, it is likely to be important to track the ball in a consistent egocentric direction relative to the head, even in the case of auditory–motor tasks such as ball trapping. Thus, it is reasonable to expect that blind footballers would utilize a strategy to couple the head direction relative to the movement of the ball during trapping.For other sports, such as cricket28 studied the movement patterns of blind footballers compared to sighted footballers in a fast and repetitive ball passing task against a wall. The authors found that the blind footballers presented a greater trunk flexion angle at the lumbar (L1/T12) and thoracic (T9/T8) levels, but not at the cervical (T1/C7) level, when compared to those of sighted individuals while performing passes. They imply that forward leaning of the trunk seems to be a strategy related to maximizing the quality of auditory inputs to guide postural control during passing/receiving the ball. However, they did not examine movement patterns, such as the head and trunk, to localize the ball position during receiving, because the study was designed to analyse movement patterns immediately before and after kicking the ball. To clarify this issue, we investigated whether downward head rotation or forward tilt of the trunk could contribute to accurate sound localization for ball trapping.Finocchietti et al.The purpose of the present study was to determine the strategy of blind footballers to localize a dynamic sound source, such as a moving ball. Specifically, we investigated the characteristics of head rotations in blind footballers compared to sighted nonathletes when trapping an approaching ball. We hypothesized that blind footballers utilize larger head rotations in order to accurately perform ball trapping.28. Their foot preferences  were self-declared; of the 12 participants, 11 were right-footed and the remaining participant was a left-footed nonathlete. The group of “blind footballers” included totally blind and low-vision individuals who played, and regularly trained in blind football. Three players were in B1; two players were in B2; one player was in B3, according to the classification rules of the International Blind Sports Federation29. B1 players are those who have a visual acuity lower than LogMAR 2.6, B2 players are those who have visual acuity ranging from LogMAR 1.5–2.6 and/or visual field constricted to a diameter of less than 10 degrees, and B3 players are those who have visual acuity ranging from LogMAR 1.4–1.0 and/or visual field constricted to a diameter of less than 40 degrees. The characteristics of the blind footballers are shown in Table Participants were blind male footballers  and age-matched healthy sighted nonathletes . This study adopted its experimental design, comparing blind footballers with sighted control groups, based on a previous study28, because this reflects an actual condition in playing blind football and therefore has an ecological approach. The floor of the room was covered by joint mats  to prevent the risk of injury by fall. Thin threads were attached to the mat surface to provide the participants standing on the mat with spatial information about the original position. The reference point was defined as the intermediate position between the two threads. An infrared camera motion system with 10 cameras  was used to compute the three-dimensional position of reflective markers attached to the body of each participant. The cameras were placed around the ball and the participant's body , one marker on each shoulder, each greater trochanter, each lateral epicondyle of femur, each lateral malleolus, each toe, and each heel.Figure The official ball approved by the Japan Blind Football Association was used in the experiment. The ball, with infrared reflective tape, was launched to the participants using a self-made apparatus, which contained an aluminium rail to adjust the ball speed and direction. The inclination of the rail was 45 degrees to the ground. The ball was released manually by the experimenter from one of three different height positions on the rail, such that the ball speeds were 2.4 m/s, 2.2 m/s, and 1.92 m/s. The distance between the ball launching point and the reference point was 4.5 m. The ball direction  was changed by adjusting the direction of the rail trial-by-trial to prevent the participants from anticipating the ball direction prior to launching. Moreover, there was some noise each time the rail was moved by the experimenter. For this reason, the experimenter intentionally generated the noise by moving the rail for each trial, even when a ball was continuously launched to the same direction as the previous trial, so that we could prevent participants from anticipating the ball direction prior to launching. Four directional conditions were set as shown in Fig. The participants were instructed to stand at the original position wearing socks. They were blindfolded with an eye mask during the task to prevent them from gaining knowledge of the experimental setup. The participants performed trapping an approaching ball by using their right foot in the natural condition, without instruction on head movements. They were instructed to trap the ball at their feet as accurately as possible. The participants returned to the original position after ball trapping to confirm that they were ready for the next trial.The participants performed the ball trapping task on different types of trials, that differed according to the ball speed and direction. A total of 12 practice trials were performed: Three trials for each of the three different speeds , and four different directions  in order to familiarize themselves with the task. After the practice trials, the participants completed 36 experimental trials . The order of the ball speed and direction was counterbalanced. Participants had a 5-min break between the blocks. All participants completed a total of 48 trials during the experiment.θHDs) was derived from two vectors  was derived from two vectors  was derived from two vectors  was derived from two vectors  was used to calculate the kinematic variables. Some variables related to head and body movements were defined: Head rotation angle in the sagittal plane , head rotation angle in the horizontal plane , trunk rotation angle in the sagittal plane, and ball angle. The head rotation angle in the sagittal plane ; this was accomplished by resampling the time of each trajectory using the interp1 function of MATLAB. The head rotation angles in the sagittal plane relative to those at the time of ball launching were also calculated for each 10% time point.In order to explore the relationship between the head direction and the ball position during ball trapping, the coefficient of correlation value between the angle of head rotation in the sagittal plane and the ball angle was measured as variable of head-ball coupling. As a valid analysis for head-ball coupling, our study applied the method of correlation analysis, which was used to reveal a correlation between head directions and bat positions at the time of bat-ball contact in the previous studyWith regards to performance variables, the absolute error (AE) and variable error (VE) were calculated from the distances between the centre of the ball and the midpoint between the toe and the heel on the right foot at the ball trapping point. If the right foot did not make contact with the ball, that is, the ball passed by the participant’s foot, the error value was calculated based on the local minimum between the distances on the x-axis. AE was defined as an absolute value of the distance between the centre of the ball, and the midpoint between the toe and the heel on the right foot on the x-axis. VE was defined as the standard deviation of the constant error, which was calculated by the distance between the centre of the ball and the midpoint between the toe and the heel on the right foot on the x-axis. These performance variables of the ball trapping task did not seem to be affected by footedness . In fact, the left-footed participant's performance within the sighted group was 3rd and 4th in AE and VE, respectively. It was clear that a significant negative result was not found in the participant; the data were therefore treated in the same way as for the other participants.p > 0.050) based on the analysis performed by the Finocchietti et al.28, and Levene's test was used to assess the homogeneity of variance (p > 0.050). A two-tailed Student’s t-test was used to compare the variables between blind footballers and sighted nonathletes. The nonparametric test (two-tailed Mann–Whitney U-test) was used when the assumption of normality was violated. A repeated measures ANOVA (3 blocks) was used to confirm whether practice effects led to improvements in task performance through 3 blocks  in the sighted nonathletes who were not familiar with performing the ball trapping task. No significant main effects of the block were confirmed either on AE or VE; therefore, the data of 36 trials in the AE and the VE of the sighted nonathletes were combined and analysed. Data of one trial from two sighted nonathletes were excluded from the actual analysis as they were not recorded correctly. Analysis was conducted using IBM SPSS Statistics software . The alpha level was set at 0.05.The Shapiro–Wilk test was used to assess whether the data were normally distributed (p < 0.001) than that of the sighted nonathletes (11.52 ± 1.57 cm), as shown in Fig. p < 0.001) than that of the sighted nonathletes (13.66 ± 1.27 cm), as shown in Fig. The AE of the blind footballers (5.37 ± 1.02 cm) was significantly smaller  between the blind footballers (− 3.1 ± 5.8 deg.) and the sighted nonathletes (1.7 ± 6.9 deg), as shown in Fig. p = 0.036) between the blind footballers (− 37.3 ± 17.2 deg.) and the sighted nonathletes (− 14.3 ± 15.8 deg.), as shown in Fig. p = 0.030) between the blind footballers (− 36.2 ± 14.5 deg.) and the sighted nonathletes (− 18.8 ± 8.4 deg.), as shown in Fig. With regards to the head rotation in the sagittal plane, there was no significant difference in the head angle at the time of ball launching . Furthermore, the relative angles of the head rotations in the sagittal plane at each time point were significantly larger in the blind footballers than those in the sighted nonathletes at all time points  between the blind footballers (− 18.2 ± 10.1 deg.) and the sighted nonathletes (− 17.0 ± 17.8 deg.), as shown in Fig. p = 0.275) between the blind footballers (− 20.4 ± 8.6 deg.) and the sighted nonathletes (− 12.7 ± 14.1 deg.), as shown in Fig. p = 0.554) between the blind footballers (− 13.0 ± 3.2 deg.) and the sighted nonathletes (− 12.0 ± 2.5 deg.), as shown in Fig. With regards to the trunk rotation in the sagittal plane, there was no significant difference in the trunk angle at the time of ball launching  between the blind footballers (2.4 ± 3.0 deg.) and the sighted nonathletes (− 0.8 ± 1.7 deg.), as shown in Fig. p = 0.689) between the blind footballers (22.8 ± 5.7 deg.) and the sighted nonathletes (20.1 ± 15.0 deg.), as shown in Fig. p = 0.979) between the blind footballers (25.7 ± 3.8 deg.) and the sighted nonathletes (25.6 ± 14.1 deg.), as shown in Fig. As for the head rotation in the horizontal plane, there was a significant difference in the head angle at the time of ball launching  was the main task, wherein the trunk flexion angle was extracted from data averaged between − 250 and 250 ms around the foot contact with the ball. For the reason, it is possible that the forward tilt of the trunk observed in the blind footballers may be attributed to a specific movement to kick the ball, rather than localize it. In contrast, receiving the ball was the main task in the current study; thus, localization of the ball was necessary, and it seems that the blind footballers used a strategy to rotate the head towards the ball in order to accurately localize it. The present study has added a new finding to this field, in that the strategy of blind footballers to accurately localize a ball in trapping is not attributed to the forward tilt of the trunk, but rather to the larger downward head rotation. The strategy observed in the present study could be specific to the ball trapping task. It is expected that further studies will lead to a greater understanding of a strategy for sound localization in other auditory–motor tasks related to the actual playing of blind football.A previous study has suggested that the forward leaning of the trunk observed in blind footballers could be used as a strategy to maximize the quality of auditory inputs to guide postural control during passing/receiving a ball28. More than just localizing the sound source, blind footballers can also develop strategies for interacting with that sound source through their training in blind football. Indeed, it is possible to assume that the present task is not only about localizing a sound, but also to interact with the source of sound. This interaction affects the manner that the players perceive the sound and its location. This assumption is in accordance with the common coding approach to perception and action38 and with the theory of event coding39. According to these approaches, perceived events and planned actions share a common representational domain, and therefore, the manner one perceives events is influenced by his/her typical or intended interaction with them. From these findings, it seems that blind athletes can use a strategy to couple the perception of a dynamic sound source and the planned action for trapping. Thus, the planning of ball trapping should indeed be different between the blind footballers and the sighted nonathletes, not only because the blind footballers are thought to be more accurate in localizing the sound source, but also because their typical interaction with that sound source differs from that of the sighted nonathletes. For these reasons, it is reasonable to explain that the large downward head rotation of the blind footballers is due to the experience of playing blind football.A previous finding has suggested that blind footballers can develop specific strategies to localize a dynamic sound to maximize the quality of auditory inputs, due to long-term training in blind football21. Pointing accuracy to auditory targets was higher under the long sound duration condition, in which listeners showed a larger amplitude of head movements  and a larger final heading angle towards targets21. The authors suggested that the accuracy of pointing to long stimuli could be due to the contribution of heading towards the target, thereby providing a more accurate frame of reference for the anticipated control of pointing. They also suggest that the heading direction is coded in a body-centred reference frame, and can be used directly by the reaching motor command that shares the same reference frame; the results of the present study are in agreement with those of these previous studies. The fact that the sighted nonathletes were blindfolded during the task could lead to an awkward or inefficient posture and worse auditory–motor performance. A previous study compared the postural control of blind footballers to sighted footballers and sighted individuals during unstable standing balance tasks under closed-eyes conditions, showing no difference of the balance performance between the blind footballers and the other groups before and after training40. Therefore, it seems that the lower performance in the sighted nonathletes did not necessarily result from an awkward or inefficient posture due to the blindfolded condition. Our results indicate that precise ball trapping in blind footballers can be not only due to the accurate frame of reference by head rotation towards the ball, but also the head-centred reference frame that is similarly shared and used by the motor control of the foot in ball trapping.With regards to the auditory–motor performance of ball trapping, the blind footballers showed a better performance compared to that of the sighted nonathletes. The accuracy of auditory–motor performance, such as reaching and pointing to auditory targets, has been shown to be influenced by the position of the sound source in relation to the head25. For instance, elite baseball batters have been found to rotate their heads until bat-ball contact, indicating the possibility that they made head rotation according to the prediction of ball trajectories24. Elite cricket batters have also been found to have a tighter coupling between the ball and the head, such that the ball was kept in a consistent egocentric direction throughout batting22. The study by Mann et al.22 indicates the functional advantage of this behaviour to keep the target in a consistent direction relative to the head, since visuo–motor tasks, like catching and hitting, are understood to be controlled in an egocentric manner. These findings also highlight the importance of keeping the ball in a consistent egocentric direction relative to the head in the auditory–motor task, which requires the prediction of ball trajectories and interception of the ball. Spatial location of an object is, in principle, coded with an egocentric and allocentric reference of frames41. Though sound location can be represented in multiple coordinate frames43, it is mainly coded in a single head-centred reference frame27 that is processed based on auditory cues, such as interaural level and time difference cues, and monaural spectral cues44. These previous findings can explain why the blind footballers continued to rotate their head to keep the ball in a consistent head-centred egocentric direction in tracking the approaching target, in terms of its localization on the basis of auditory cues. Therefore, our study suggests that blind footballers couple the downward head rotation with the movement of an approaching ball, while ensuring that the ball was kept in a consistent egocentric direction relative to the head throughout ball trapping.No significant difference in the groups was found regarding the coefficient of correlation value between the head rotation angle and the ball angle; this demonstrates that both groups rotated their heads downward according to the approaching ball. However, the relative angle of the downward head rotations in the sagittal plane at each time point was significantly larger in the blind footballers than in the sighted nonathletes from the early time point after ball launching to the moment of ball trapping. These results may indicate that the blind footballers kept the ball in a more consistent direction relative to the head throughout the ball trapping phase. Previous studies report a strategy of head-ball coupling that couples the head direction to the movement of the ball to track the target in skilled batters45. In general, binaural cues, like interaural time and interaural level differences, are mentioned as the primary cues for sound localization in the horizontal plane46. Even though the ball direction was random in each trial in the present study, the initial point of the ball launching remained constant. It may be possible that the blind footballers could prepare for quick prediction of the ball trajectory based on auditory cues provided by the slightly increased horizontal head rotation angle at the time of ball launching.The head rotation angle in the horizontal plane at the time of ball launching was slightly, but significantly larger in the blind footballers than that in the sighted nonathletes. Differences in the timing and intensity of sounds arriving at the two ears are well-documented cues that can be used to judge the direction of the sound source49, pitch discrimination52, and sound motion53, indicating that the abilities of blind individuals are assumed to be attributed to compensating for visual loss. Recent findings suggest that rapid and accurate identification of sound direction in blind footballers can be due to long-term training in blind football8. Furthermore, Velten et al.4 reported that blind footballers are more precise than blind individuals in terms of the identification of sound direction; this indicates that the results are not solely due to the absence of vision and enhancement in auditory perception accuracy, but are also related to the practice of blind football. Regarding the years of blind football playing experience, Mieda et al.8 demonstrated that the more experienced group showed a tendency to identify sound direction more rapidly than did the less experienced group. Thus, their results indicate that rapid identification of sound direction in blind footballers can be attributed to a long period of blind football playing experience. Taken together, it is reasonable to assume that the long-term experience of blind football, but not the visual impairments, could enable the blind footballers to localize the ball more accurately than the sighted nonathletes.Various studies have reported that blind individuals have supra-normal auditory abilities in comparison to sighted individuals regarding sound localization53. Another possibility which may be considered is that blind individuals use the egocentric frame of reference due to the loss of vision when localizing a sound55, which could result in keeping a moving ball in a consistent egocentric direction relative to the head. Future studies could address this question by clarifying the characteristics of head rotation of blind footballers compared with blind individuals during ball trapping.Despite the present findings, the question remains whether the large downward head rotation adopted by the blind footballers was due to the lack of vision. If this is the case, blind nonathletes should present a similar pattern, even with differences in the performance of ball trapping. One possibility for this is that blind individuals may focus on self-induced motion of the surrounding sound sources resulting from active head and/or body movements much more intensely than sighted individuals to utilize the reliable information about the deviation between perceived and physical sound-source locationsThe present study demonstrated a higher performance of ball trapping and a larger angle of downward head rotation in the blind footballers compared to the sighted nonathletes. However, no significant difference in trunk rotation angle was found between the groups. These results suggest that blind footballers use a larger downward head rotation as a strategy for precise ball trapping, ensuring localization of the ball towards the front of the head. These results also suggest that the strategy of blind footballers to accurately localize a ball in trapping is not attributed to forward tilt of the trunk, but rather to downward rotation of the head. The relative angle of the downward head rotation of the blind footballers was consistently larger than that of the sighted nonathletes from an early time point after ball launching to the moment of ball trapping. Our study suggests that blind footballers couple the downward head rotation with the movement of an approaching ball, ensuring the ball is kept in a consistent egocentric direction relative to the head throughout ball trapping.


Based on Navier–Stokes equations, a numerical model for studying the dynamic responses and mooring forces of the moored Submerged Floating Tunnel (SFT) driven by surface waves is presented in this paper. The mechanics models of the vertically and inclinedly moored floating body under wave forces are built, and the overset meshing method is employed to dynamically configure the computational meshes. Two laboratory experiments are used for validating the numerical model in terms of motion responses and mooring forces of the SFT, indicating the proposed model is capable of accurately simulating the instantaneous position of the body under the wave action. This hydrodynamic model is then utilized to simulate the wave–structure interaction of the prototype SFT designed for Qiongzhou Strait located between Mainland China and Hainan Island. The effects of the fundamental structure parameter, or the inclined mooring angle (IMA), on the dynamic responses of SFT are analyzed. The numerical experiments not only shed light on the mooring forces, as well as pitch, sway and heave responses of the SFT with various values of IMA, but also provide guidance for the choice of IMA in engineering design. The range of IMA is separated into five zones, and Zone 2 is regarded as the best choice for the design of IMA for both motion displacements and mooring forces are relatively small in this zone. Zone 3 is considered to be the worst choice as not only are motion responses of SFT severe in this zone, but also the mooring chains are at the risk of going slack under severe wave conditions. The characteristics of SFT are not burying under or putting upon waterbed but a tube-like floating tunnel at a certain water depth supported by its self-buoyancy and constrained by a mooring system anchored to the waterbed. Figure 10. Although SFT has been proposed as an effective traffic solution to cross waterways, such as the Strait of Messina in Italy, Hogsfjord in Norway, South Sea of Korea, Funka Bay in Japan, Qiongzhou Strait in China, Bohai Strait and Taiwan Strait in China15, it has yet to be realized due to a lack of safety assurance. For an SFT to be safe during its whole life, it is important to develop efficient and accurate numerical models to determine the hydrodynamic loads on the SFT and its potential motions in response to extreme wave conditions.Recently, the interest in Submerged Floating Tunnel (SFT), which is also named Archimedes Bridge, has increased as coastal and ocean engineers search for an innovative transportation concept for crossing the deep strait, lake, fjord and other deep and long waterways17, motion responses21, mooring forces26, velocity fields28 and so on. These experiments not only shed light on the influences of hydrodynamic and structure parameters on motion responses as well as forces acting on the small size structures, but also provide guidance for the protection and design of the structure. Assuming the flow was non-viscous and irrotational, earlier studies mainly used the potential flow theory to simulate the dynamics of the floating body. Based on potential theory, Koo and Kim30 built a 2D numerical wave tank to study the fierce interactions between stationary or freely floating bodies and surface waves. Kunisu31 also utilized Morison’s equation based on potential theory to evaluate the wave forces on SFT, and the results indicated that inertia force and drag force simultaneously worked on the structure. Guerber et al.32 successfully used the fully non-linear potential flow (FNPT) model to simulate the fully nonlinear interaction of waves with a submerged horizontal cylinder. Subsequently, the model in Guerber et al.32 was extended by Dombre et al.33 to solve freely floating bodies on the free surface, and the accuracy and convergence of the extended model in solving wave–structure interactions were demonstrated. Nevertheless, as the convection potential flow method assumes an irrotational flow, the nonlinear interactions of waves with obstacles, including flow separation, vortex generation, and shedding, are difficult to determine satisfactorily. Besides, this type of model is not capable of predicting the pitch motion of an SFT caused by viscous damping in the vicinity of the structure, although a good agreement of the sway and heave motions are gained.Over the years, extensive studies on nonlinear wave–structure interactions have been conducted and numerous conclusions have been made based on both experimental and numerical methods in the design of SFT and other floating structures. In laboratory experiments, many monitoring results are gained by laboratory instruments, such as wave forces39. Most of these studies listed above only dealt with the interactions between water waves and fixed structures without considering the influence of motion response on wave–structure interaction. One of the key issues for solving the N–S equations in the treatment of the varying positions of the structure during the interaction is how to deal with the body motion in the computation. Because the body surface is a part of the boundary of the fluid domain, it is necessary to update the computation mesh according to the geometry change in the fluid domain resulting from the body motion. A mesh deforming method40 is commonly used to handle the mesh update, but mesh quality might be reduced severely when the body undergoes large motions41. The method of adaptive mesh refinement42 is suitable for arbitrary motions of a body, while the calculation is time-consuming and mesh quality is unable to be guaranteed in the long period of body motion43. A layering mesh method based on CFD software package, Fluent, has been successfully developed to study the interaction between bridge decks and incident waves by User Defined Function45, while the structure is only allowed to move in one direction. An efficient method for preserving good mesh quality in the simulation of body motion, especially large body movements in a long duration, is the dynamic overset mesh technique, which has been successfully applied to practical hydrodynamic problems involving structure–wave interactions47.With the development of computer technology over past decades, the latest computers are now capable of carrying out a direct numerical simulation of the wave–structure interaction based on the Navier–Stokes (N–S) models.22 successfully developed a porous body model coupled with the Volume of Fluid (VOF) method to predict the wave deformation and dynamics of the SFT in a small size, while the model suffered from high computational cost in the grid generation and re-meshing. Subsequently, Peng et al.24 applied the Immersed Boundary Method (IBM) to deal with the movable SFT under waves, and the numerical model based on Eulerian grid methods had difficulties in treating structures with complex geometries. Ren et al.48 applied a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and the SFT, a good agreement was gained between numerical results and experimental data except for the prediction of the transmitted wave with a maximum under-prediction of 40%, which was correlated with the artificial viscosity used in momentum equations.In order to protect the floating structure, tensioned mooring systems are often used to restrain the motion of the body, and an accurate prediction of the mooring forces, as well as motion responses, are critically important for the structure design. As mentioned above, numerical methods based on potential theory are inadequate for the prediction of the multiple motions and velocity field around the body, researchers are using the N–S model to predict the instantaneous nonlinear interaction. Rahman et alSo far, as for such a novel SFT, researchers are still searching for an efficient method to accurately predict the instantaneous wave–structure interaction. Besides, researches on the performance of a prototype SFT in severe wave conditions are still scarce at present. Hence, the objective of this paper is to first develop an efficient method based on the N–S model to simulate the interaction between incident surface wave and moored submerged floating tunnel, then analyze and quantify the performance of a moored prototype SFT under severe wave conditions. The CFD software package, FLUENT 17.0, is utilized as a basic solver in this model, and User Defined Function (UDF) written in C programming language is incorporated into the model to solve the motion equations and control the body motion. The overset method is utilized to handle the mesh updating, which is supported by the software package. This paper is organized as follows. “u and v are the velocity components in the x-direction and the y-direction, respectively; g is the gravitational acceleration; p is the fluid pressure;x-direction and y-direction, respectively.In this study, the employed numerical wave tank used to simulate the interaction between submerged floating body and incident wave is based on the N–S solver. The flow of an incompressible viscous fluid, as shown in Fig. uc and vc in the relaxation zones asr stands for the relaxed solution value, subscript i stands for the predefined incident value. The schema of a numerical wave tank is shown in Fig.  in Eqs.  and 6),,uc and vC(x) with respect to x in the front wave generation zone and front wave absorption zone. As the relaxation scheme is utilized in the front wave generation zone and front wave absorption zone in the flow, momentum sources In the front wave generation zone,  to Eqs. –6, Fig. mentclass2pt{minim49. The porous media method developed in the present work is a simulation of the physical energy dissipation mechanism. For this aim, the momentum source term composed of a viscous dissipation term and an inertial term is added to the Navier–Stokes equations as follows:ith momentum equation, To avoid wave reflection from the outlet boundary, one porous wave absorber is prescribed at the outlet to absorb wave energy before reflection occurs.50.By incorporating the momentum source defined by UDF into the CFD solver, we can model the numerical wave tank in the present study. Further information about the validation of the numerical wave tank can be found in Chen et alThe dynamic motions of the floating body are driven by incident waves in combination with mooring chains. Thus, the correlation between forces acting on the moored body and motions of the moored body should be gained to establish the mechanics model of the floating body. The instantaneous position of the vertically moored floating body during its interaction with a wave is shown in Fig. LM is the length of the mooring line and Furthermore, as the vertically moored floating body does not rotate during its interaction with incident wave, the summation of the moments acting on its center of gravity should be zero, i.e.,On the other hand, when the body is anchored to the bottom of the wave tank with inclinedly aligned mooring lines, the dynamics of the floating body at any instantaneous position is shown in Fig. Considering the no-slack condition of the mooring lines, the geometric feature of the wave–structure interaction in Fig. 51. A schematic drawing of overlapping component and background mesh zones is shown in Fig. The overset mesh, also known as Chimera or overlapping mesh, is used to facilitate the motions of the floating body due to the incident waves in this study. Compared with traditional rigid and deforming mesh options in the software package, the overset mesh is a very effective way of preserving high mesh quality in the process of fierce fluid–structure interaction with large motion displacements. In the overset meshing methodology, two regions, background and component meshes are created. The meshes in each cell zones are independent as these cell zones are not forced to be aligned with each other. In the process of hole cutting, the cells at the overlapping zones are deactivated, and different cell zones are coupled by an interface to provide continuous solutions. The deactivated cells in the hole cutting are called the dead cells. The donors are the cells that supply flow information to the associated overlapping cell zones. Receptors obtain information from the donors in the corresponding overlap cell zone and vice-versa51.The overset meshes move together with the floating body, thus no mesh deformation exists in the duration of motion responses. The background meshes keep stationary in space and the overset meshes are free to move as long as the cells in the overlap zones work well. The cells in the overlapping region are solved simultaneously by the discretized governing equations on the overset mesh boundaries. Thus, the coupling between the meshes is implicit. In the interpolation method, receptor cells at the overset interface obtain messages from nearby donors, which can be interpolated by the following equationIn the solver, the governing equations are discretized based on the finite volume method (FVM). The Second Order Upwind algorithm is used to discretize the momentum convection. Coupled algorithm is used for the pressure–velocity coupling with Pressure Staggering Option (PRESTO) discretization scheme. The Volume of Fluid (VOF) method is adopted to capture the fluctuating water surface. The laminar model is used to simulate the incompressible and viscous flow.The procedure for solving the interaction between wave and moored floating body is described as follows. At the very beginning of every time step, the flow field is solved by the main program firstly. Then the wave forces and moments are obtained by using the User-Defined Functions with an incorporated C programming language to integrate the pressure and shear stress over the floating body. For the vertically moored floating body, Eqs. –13 are tmentclasspt{minimady, Eqs. –17 are t24 are adopted to validate the capability of the proposed model. The experiments are carried out in a two-dimensional wave tank at Nagoya University, and Fig. 22 and 60° in the second experiment24. Figure Two available laboratory tests.22 and Peng et al.24.The weight of the floating is assumed slight compared with the buoyancy force acting on it so that the mooring lines always remain in tension during the interaction between the moored body and the incident surface wave, which avoids the impulsive force acting on the mooring chains. If the mooring chains become slack, the impulsive force develops on them and it may cause the failure of the mooring lines easily. Moreover, the slacking of the mooring lines causes the dynamic movement of the moored body more complex. For details about the experimental set-up, the reader is referred to Rahman et aldx = wavelength/80 and dy = wave height/15 for the near water surface zone as the mesh resolution in background mesh. In the component mesh, we finally chose dx = minimum  and dy = minimum  for the zone near the floating body. The courant number is chosen as 0.1 in the whole computational period.In the numerical model, model sensitivity tests have been conducted with different grid resolutions and courant numbers related to the time step. In the background mesh, we finally chose In the case of the mooring lines anchored vertically, there occurs no pitch displacement of the body and only the sway and heave values are gain in the wave–structure interaction. Figure x-axis. On the other hand, the negative sway magnitudes represent horizontal displacements of the floating body along the direction of the negative x-axis. The positive heave values represent its displacement along the upward direction and the negative heave values represent its displacement along the downward direction. In Fig. The positive sway magnitudes represent horizontal displacements of the floating body along the direction of the positive t1–t5. At t1 stage, the moored body stays in its initial place, and both sway motion and heave motion equal to zero. Subsequently, the body moves in onshore direction under external wave forces and mooring forces before it reaches its maximum sway displacement at t2 stage, where the heave displacement also reaches maximum. The body departs from the maximum displacements point and moves back to its initial place at the states between t2 and t3. Time series of sway motion in the second half wave cycle from t3 to t5 are similar to that in the first half wave cycle from t1 to t3. Two pairs of peak and valley values for the heave motion are observed in Fig. t1 to t3 is longer than the second half wave cycle from t3 to t5, implying the vertically moored floating body experiences a longer onshore movement than offshore movement, which is closely correlated with the strongly nonlinear and fierce wave–structure interaction.To distinguish the results more clearly, five lines are drawn to mark different time instants in one period, namely, t1 when no motion responses of the body happen. In the figure, it is seen that the wavefront is passing over the floating body and the body moves in the onshore direction due to wave forces from t = 0–0.285 T. The body then gradually moves to the reverse direction and comes back to its initial position at around t = 0.654 T. After that, the floating body moves to the offshore side and returns to its initial position from t = 0.708 T–0.931 T. Vortex first appears on the top of the body between t = 0.285 T–0.362 T, and disappears at t = 0.654 T, which is attributed to the wave overtopping and wave breaking on the top of the body. It is also observed that vortex appears around the sharp corners of the floating body at other instants, while the phenomenon is not obvious, which is probably attributed to no pitch motion of vertically moored floating body happens during wave–structure interaction. The magnitude and direction of the water particle velocities on the onshore side change abruptly near the free surface compared with that on the offshore side, which is caused by the fact that the wave energy is partly dissipated and reflected by the floating body, and transmitted wave energy forms secondary wave crest in the rear area of the body.In order to illustrate the details of the wave–structure interaction, instantaneous water surface profiles, and velocity vectors around the vertically moored body for different stages in one wave cycle is presented in Fig. Time series of numerical results about the dynamic motions of the inclinedly moored floating body as well as mooring forces acting on it are verified with measured results from the experimental data in Case 2, which is presented in Fig. t1–t5. At t0 stage, the moored body stays in its initial place, and all motion responses, including sway motion, pitch motion and heave motion, equal to zero, while the peak values of mooring forces have slight phases difference with motion responses, especially onshore mooring force. The floating body at t1 stage is quickly changing its position as the motion velocities calculated from motion time series are largest in a wave cycle. At t2 stage, three motion responses reach peak values at the same time, and no phase difference is found in the time series of mooring forces as they all reach valley values. As the body departs from the maximum displacements point, the mooring forces increase to the peak value again at an instant close to t3 stage. Time series of body motions except for heave motion in the second half wave cycle from t3 to t5 are similar to that in the first half wave cycle from t1 to t3. For mooring forces, the valley values happen at the stage when the moored body is in the largest motion response, while the peak values appear at the instants close to the initial position.To distinguish the results more clearly, five lines are drawn to mark different time instants in one period, namely, t1 to t3 is longer than the second half wave cycle from t3 to t5, which is attributed to the strongly nonlinear and fierce wave–structure interaction.It should also be noted that two pairs of peak and valley values for the mooring forces and heave motion are observed in Fig. t = 0.13 T to 0.25 T. After that, the body gradually moves in the reverse direction and comes back to its initial position at around t = 0.58 T, and the movement in the first half wave cycle is finished. The offshore movement in second half wave cycle is similar to the motion in the first half wave cycle except that the duration of the second half wave cycle is smaller, demonstrating once again that the onshore movement lasts longer than offshore movement in each wave period.In order to illustrate the details of the wave–structure interaction, instantaneous water surface profiles, and velocity vectors around the inclinedly moored body for different stages in one wave cycle is presented in Fig. .27. It is also noteworthy that rotation directions of the vortexes do not always follow the rotate motion of the body, and phase lags exist between them. Overall, the proposed model gives a good prediction of the velocity field around the body.The details of velocity field around the body are also illustrated in Fig. 52.Recently, Hainan Free Trade Zone in China has been established to further promote the local economic development, while traditional transportation method, i.e., ship, aircraft, is getting more and more difficult to satisfy the rapidly increased demand of transportation between Mainland China and Hainan Island. As seen in Fig. 15. Figure 52.Qiongzhou Strait is one of the largest three straits in China. The length is about 80 km from east to west, and the width ranges from 18 to 35.5 km (29.5 km on average) from north to south. The marked line in Fig. x-axis when SFT is at its equilibrium position, has a great influence on the constraint of SFT, and it is regarded as a key parameter of SFT10. Hence, to have a better understanding of the motion responses of prototype submerged floating tunnel under waves, we employ the numerical model validated in previous sections to study the influence of IMA on the prototype SFT in Qiongzhou Strait. According to local environmental conditions of Qiongzhou Strait, the wave height with a 25-year return period is 7.1 m, and the corresponding average wave period is 8.7 s, and for a 100-year return period, the wave height and wave period are 8.6 m and 9.6 s, respectively53. Taking these extreme wave conditions as a reference, 18 cases are designed for the numerical simulation as shown in Table Inclined mooring angle (IMA), which is the initial angle between SFT tether and The simulated results of mooring forces as well as motion responses with IMA varying in the range of 25°–90° under two extreme wave conditions are presented in FigsThe ordinate values in the subfigures of mooring forces in Fig. To distinguish the results more clearly, four lines are drawn to separate the range of IMA into five zones as shown in Fig. 10.As seen in Fig. Figure 54 proposed a dimensionless number for the dynamic plastic response of beams and plates, which reflected three aspects, i.e., the inertia of the distributed loading, the resistance ability of the material to the deformation and the geometrical influence of the structure. The dimensionless number, termed as response number, is defined by the following equations.For the study of dynamic plastic response of beams and plates subjected to uniformly distributed pressure, ZhaoThe boundary condition of the freely floating tunnel under wave action is free-free, and the plastic displacement, When t of Eq.  can be eThe distributed net pressure around the tunnel surface is nonuniform. To get an approximation of the deformation of the tunnel under wave action, the distributed net pressure is assumed to be uniform, which is proportional to the resultant forces in both horizontal and vertical directions. As the amplitudes of sway motion are much larger than heave motion shown in Fig. e in Eq.  is very Based on Eq. , the lim to Eqs. –21. Besi to Eqs. .In this paper, a numerical model for studying the motion responses of vertically and inclinedly moored SFT with multiple degrees of freedom under wave forces is proposed. The N–S equations are used as the governing equations to describe the flow field. In the numerical wave tank, two wave absorption zones are distributed in the front and rear of the SFT to absorb reflected waves and transmitted waves, making sure the working zone is not affected by reflected waves. A description of the methodology focusing on the mechanics of the vertically and inclinedly moored floating body is presented in this paper. To preserve the mesh quality around the body during the entire computation, overset meshing methodology is utilized in the numerical simulation and high mesh quality is preserved in the process of fierce fluid–structure interaction.Two laboratory experiments are used for validating the numerical model focusing on a vertically moored floating body and inclinedly moored floating body, respectively. A good agreement is gained by comparing the simulated results with measured data in terms of motion responses and mooring forces, indicating the proposed model is capable of simulating the interactions between surface waves and SFT constrained by mooring chains. It is found in the results that the onshore movement in the first half wave cycle from lasts longer than offshore movement in the second half wave cycle for both vertically and inclinedly moored body in each wave period, implying the interaction is strongly nonlinear and the body experiences fiercer motions along the direction of wave propagation. It is also found that vortex generates more easily around the corner of the inclinedly moored structure than the vertical moored structure, which is because the velocities at the corner are relatively large when the inclinedly moored body rotates around its gravity center, and flow separation is easily caused by viscous effect at the corner.The prototype SFT under severe wave conditions of a 25-year return period and 100-year return period designed for Qiongzhou Strait located between Mainland China and Hainan Island has been simulated using the verified hydrodynamic model for wave–structure interaction. The numerical simulations shed light on the offshore and onshore mooring forces, as well as pitch, sway and heave responses of the SFT under different IMA conditions. It’s seen that peak values exist in three motion responses, and the corresponding mooring forces also reach to local maximums and minimums. Large mooring forces means a high requirement for the strengths of mooring chains and anchoring, and small mooring forces may also bring damage to the mooring system for the possibility of the slack phenomenon. To provide guidance for the design of IMA, the range of IMA is separated into five zones. Zone 2 is regarded as the best choice for the design of IMA for both motion displacements and mooring forces are small in this zone, while Zone 3 is considered to be the worst choice as not only are motion responses of SFT severe in this zone, but also the mooring chains are at the risk of going slack under severe wave conditions.


A parameter study of laboratory X-ray diffraction contrast tomography (LabDCT) has been performed to clarify the effects of various experimental parameters on the 3D reconstruction of the grain structure. Recommendations for optimizing LabDCT experiments are given. GrainMapper3D, which produces a 3D reconstruction from binarized 2D diffraction patterns. It is found that the exposure time directly affects the background noise level and thus the ability to distinguish weak spots of small grains from the background. With the assistance of forward simulations, it is found that spots from the first three strongest {hkl} families of a large grain can be seen with as few as 30–40 projections, which is sufficient for indexing the crystallographic orientation and resolving the grain shape with a reasonably high accuracy. It is also shown that the electron current is a more important factor than the accelerating voltage to be considered for optimizing the photon numbers with energies in the range of 20–60 keV. This energy range is the most important one for diffraction of common metals, e.g. iron and aluminium. Several suggestions for optimizing LabDCT experiments and 3D volume reconstruction are finally provided.Laboratory diffraction contrast tomography (LabDCT) is a recently developed technique for 3D nondestructive grain mapping using a conical polychromatic beam from a laboratory-based X-ray source. The effects of experimental parameters, including accelerating voltage, exposure time and number of projections used for reconstruction, on the characterization of the 3D grain structure in an iron sample are quantified. The experiments were conducted using a commercial X-ray tomography system, ZEISS Xradia 520 Versa, equipped with a LabDCT module; and the data analysis was performed using the software package  In order to ensure that enough diffraction spots are present to index the crystallographic orientations and resolve the grain shapes with a high resolution, typically at least 120–360 projections are used. LabDCT measurements can thus take 5–10 h or even days.hkl spot from a grain can be seen multiple times at different rotation angles, as they come from X-rays with different energies and at different angles  plane of the same grain affect reconstruction is unknown, especially if some of these spots are redundant and can be skipped by reducing the number of projections. Additionally, the highest X-ray tube power is normally chosen to maximize the photon flux at each energy bin of a polychromatic X-ray spectrum. However, the spectrum of the polychromatic beam itself is affected also by the input accelerating voltage , exposure time and number of projections, on the quality of the 3D reconstruction by conducting a series of LabDCT measurements on the same sample volume. The X-ray energies and intensities of individual diffraction spots from the same grain are determined with the assistance of a forward simulation model  sample used in this study was annealed at 1123 K for 2 h, after which it was fully recrystallized with an average grain size of 75 µm and a nearly random texture. The sample shape was a cylindrical rod with a height of 30 mm and a diameter of ∼0.5 mm.K lines of W in the spectrum, they are not expected to significantly affect the results since the vast majority of the X-rays used for the diffraction are generated by Bremsstrahlung.The measurements were performed using a ZEISS Xradia 520 Versa X-ray microscope equipped with a LabDCT imaging module. The sample was placed 14 mm from the source and 14 mm from the detector .The LabDCT scans were acquired with 121 projections collected in 3° steps with an accelerating voltage of 120 kV and exposure times ranging from 20 to 400 s. Reconstructions using every other and every third projection of the scan with an exposure time of 400 s were also performed. An additional scan was carried out with an accelerating voltage of 150 kV. The power applied to the X-ray tube was 10 W for all the scans, which is the maximum power allowed by the instrument to ensure a small size of the source. The electron current therefore changes from 83.3 µA for 120 kV to 66.7 µA for 150 kV. The experimental parameters are summarized in Table 1b)]. The LabDCT data used for reconstruction were then obtained by dividing the raw diffraction data by the flat-field image. After the division, the value of each pixel was multiplied by 100 to tune the majority of the values to a range that is more appropriate for image analysis (i.e. 0 to 255). The resulting image [see Fig. 2c)] has a comparatively uniform background.For each scan, a single reference image was collected with the same instrument settings but without the sample. The projection obtained from this reference scan is commonly referred to as the flat-field image and contains some of the background intensities that come primarily from the direct beam and the inelastic interaction of the direct beam with the beamstop, but nothing from the sample , similarly to what has been done in synchrotron DCT ] were used for reconstructing the 3D volume. To minimize the effects of these predefined variables on the reconstruction results, they were kept the same for all the grain reconstructions.The diffraction spots were then segmented using a background subtraction threshold of 4 followed by a filtering using a Laplacian of Gaussian (LoG) filter. A LoG filter works by first smoothing the image using the Gaussian kernel; this also removes the majority of the local noise from the image. The remaining large intensity gradients in the image are related to the spots. Rapid intensity changes are therefore highlighted by applying the Laplacian operator to the Gaussian smoothed image  planes they originate as well as the sizes, intensities and energies of the X-rays producing the spots. For the simulations, the experimentally determined 3D grain structures were used as input to calculate the X-ray energies for each diffraction spot, and to relate that to the experimentally measured intensity of the same diffraction spot. In the model, an X-ray energy spectrum from a W target was used to calculate the intensity of the diffraction spots, taking both sample absorption and detective quantum efficiency into account. More details about the analysis procedure are given by Fang et al.  and 4d)], it can be seen that the spots appear slightly dimmer and smaller for the accelerating voltage of 150 kV. Upon closer inspection it is notable that this effect is more pronounced for some spots than others.When comparing diffraction patterns of scans using different accelerating voltages  suggest that the background noise does scale with the expected behavior:i.e. the standard deviation of the normalized global background intensity) and For quantification of the global average normalized intensity level and noise of the background, the normalized intensity within a total of 100 regions containing no diffraction spots across three projections was measured. The regions were at least 10 pixels from the nearest spots and ranged from approximately 1000 to 4000 pixels in size. The results of this quantification can be seen in Fig. 5a)].The background noise level does not appear to change significantly when the accelerating voltage is changed from 120 to 150 kV, though the average background value seems to decrease slightly as the voltage is increased , the results are also applicable to the noise-reduced images , as in the latter case IBG is close to zero but Although this analysis is conducted on the LabDCT image after the division with the reference . A small part of the volume has not been successfully indexed [see Fig. 6c)]. These regions appear to be fairly randomly distributed throughout the volume. There may be several reasons for certain regions being unindexed, including the possibility that the grains in these regions are too small to generate sufficient diffraction spots.The grain reconstruction using data set E1 is shown in Fig. 6c)] and the number of projections is the highest, providing more spots for the reconstruction. It is also expected that the highest number of projections will result in a better reconstruction simply because more data are available. This reconstruction is therefore used as a reference for the other reconstructions in order to compare their relative quality. An exception to this will be made when comparing the effects of the acceleration voltage using data sets D1 and D2, since these measurements were done separately from the others and are thus more easily aligned for direct comparison. Fig. 7Data set E1 is expected to be the best compared with all the other data sets since the diffraction pattern used for this reconstruction has the most clearly distinguishable spots [see Fig. 4a)]. The number of unindexed voxels is significantly higher for the 20 s case (see Table 2b)]. The differences are most evident in the shapes of the grains, but there are also some differences in the center-of-mass positions of some grains. The number of indexed grains increases with exposure time, especially because more small grains are reconstructed, whereas the number of false positives among the small grains appears to be constant with respect to exposure time . It appears that the number of projections does not affect the grain structure much, except that more grains have been indexed with a reduced number of projections. All the additional grains reconstructed with fewer projections are small grains appearing at the edges of the volume , and the misorientation for the same grains between the two data sets is always below 0.01°, implying a very good orientation accuracy with reconstruction using 41 projections. The common volume between the volumes E1 and E3 is about 91%, indicating a reasonably good reconstruction accuracy with the 41 projections. The additional 23 grains that can be seen in the volume from the E3 data set but not in the E1 data set are all false positives. The average center-of-mass shift between the matching pairs is below one voxel (see Table 2d). Data set D1 was used as a reference when comparing with data set D2 in order to directly compare the effect of changing the accelerating voltage from 120 to 150 kV without changing the exposure time. While the number of reconstructed grains is nearly unaffected by the accelerating voltage, the grain shape appears to be significantly affected. A relatively large portion of the volume is unindexed, especially around triple junctions and quadruple points.The difference between the reconstructions using different accelerating voltages can be seen in Fig. 74.4.1.The division of each projection by its corresponding flat-field image is used in the present study, as it is suggested to be an efficient background correction procedure. This comes with the cost of losing the ‘true’ intensities of the spots, which theoretically could provide information useful for grain reconstruction as it does for synchrotron monochromatic DCT or 3D X-ray diffraction experiments. However, since the X-ray spectrum of the source and exact detective quantum efficiency of the detector are neither particularly well characterized nor stable throughout the experiment, the reconstruction algorithm used in this work does not rely on the intensities of spots. This means that the loss of information due to the flat-field correction is of no consequence for the purposes discussed here. However, there are other concerns regarding the flat-field correction, namely the potential amplification of noise in regions of particularly low intensity in the flat-field image.e.g. the insets in Fig. 9d). However, the noise levels close to the beamstop seem to be lowered by division of the flat-field projection even for data set A, owing to the background being bright enough to avoid near-zero values. Interestingly, this is also the region with the most inaccurately segmented pixels when the raw projections (i.e. without flat-field correction) are used. This is because the intensities in this region vary substantially throughout the experiment, probably because of the instability of the source. These intensity variations cannot be removed completely by the rolling median correction, resulting therefore in a large number of noisy regions in the segmented images [see e.g. Figs. 9b) and 9d)]. The reason for the clear improvement in the normalized data sets is that the magnitude of these intensity variations is significantly reduced by the division by the similarly high intensities of the flat-field image in these regions, after which the background level can be removed [see e.g. Figs. 9a) and 9c)]. The choice of whether or not to divide by the flat-field image should therefore be considered with both the exposure time and the experimental geometry in mind. It may be worthwhile to perform segmentations using both options and choose the better result for either short exposure times or geometries which will generate especially low intensities on parts of the detector, e.g. if the detector has a very high angular coverage. For the present study, it is evident that the division by the flat-field images has overwhelming advantages for nearly all the data sets.A comparison of the quality of the segmentation with and without the flat-field correction step was therefore made  can be removed by the rolling median correction process, the background noise will still affect the segmentation of diffraction spots.The quantitative analysis of the intensities of diffraction projections shows that the exposure time does not affect the average normalized intensities of the background and spots much  that the signal-to-noise ratio increases with increasing exposure time, which is strongly correlated with the ability to properly segment spots. This is in part because some weak diffraction spots [e.g. the spot in the lower inset in Fig. 4a)] can be blurred by the background noise. These spots may be missed after rolling median correction operation during spot segmentation, especially when the spots are small  and Table 2c)] and time limitations. Additionally, the background noise can affect the size and outline of the diffraction spots even for the large spots  is reduced only from 42 to 41, while the total number of spots is reduced from 240 to 98. This is because, with 121 projections, one hkl index of a grain can result in about six spots on average during a 360° rotation. The angle range covered from the left to the right side of the detector for the present setup is ∼27°. If the diffraction vector is close to the rotation axis and a spot can be followed rotating simultaneously with the sample rotation from one side of the detector to the other, the spot can be seen in every projection and the same spot can thus be seen ten times with 3° rotation interval. For the worst case scenario, where the diffraction vector is perpendicular to the rotation axis and a spot follows a θ–2θ relation, the spot can be seen only about five times. Taking the beamstop into account, one hkl index of a grain resulting in on average six spots is very reasonable. The repeated diffraction spots are redundant for indexing the grain orientation but can certainly improve the reconstruction of the grain shape [see Fig. 7c)]. At the same time, it is evident from the data set reconstructed using 41 projections that 1–2 spots per hkl index is enough for indexing the grain orientation accurately . Here it can be seen that the intensities of spots obtained with 150 kV are consistently lower than those with 120 kV for all energy ranges. Note that the X-ray energies for the same diffraction spot are the same at different accelerating voltages. The difference is larger at low than at high energies [see Fig. 10b)]. Since the electron current at 150 kV is about 20% lower than that at 120 kV, a difference of 30–40% in the energy range 20–40 keV implies that an additional 10–20% decrease can be attributed to the change in the X-ray spectrum resulting from the increased acceleration voltage. Similarly, the difference becoming as small as 4% in the energy range of 80–100 keV implies an increase of approximately 15% in the X-ray flux resulting from the changed acceleration voltage, although the net effect of the normalized intensity is reduced due to the lower electron current.The accelerating voltage primarily affects the spot intensity, in contrast to the exposure time which mostly affects the background noise ].Note also that the majority of diffraction events for the first three strongest {hkl} families can be found in Table 4The energy range can be estimated from the geometry of the setup along with Bragg’s law. For the present study, the sample-to-detector distance of 14 mm and beamstop width of 2.5 mm give the minimum scattering angle hkl} families have high structure factors, and their corresponding photon energies are low. Since most scintillator-based detectors have the highest detective quantum efficiencies for low-energy photons while the efficiency gets significantly decreased for photon energies higher than 60–80 keV  For a sample with small grains (<30 µm), a longer exposure time of (2) For a coarse-grained sample or for a quick overview of the larger grains (>75 µm) in the sample, a short exposure time as low as 20–50 s can be sufficient. Increasing the number of projections to more than 90–120 will only offer a limited improvement for resolving the grain shapes.hkl} families. Such information is valuable for the choice of the optimal accelerating voltage.(3) For a given crystal structure, it is worthwhile to conduct a forward simulation or theoretical calculation based on a real experimental geometry to analyze the X-ray energy range for the lowest 3–4 {(4) In general, a higher electron current is preferable compared with a higher accelerating voltage for a given maximum input power.(5) A forward simulation on an experimentally reconstructed volume is recommended to eliminate any false-positively indexed grains.5.In the present study, the effects of the following experimental parameters on the quality of 3D grain reconstructions using laboratory X-ray diffraction contrast tomography have been studied for a pure iron sample: accelerating voltage , exposure time and number of projections. It is found that, for LabDCT experiments performed using instruments similar to the ZEISS Xradia 520 Versa X-ray microscope where a W anode is used and the maximum tube power is fixed,(i) the exposure time plays a more critical role for the 3D reconstruction than the number of projections and accelerating voltage, and should be prioritized for a given experiment;(ii) a low number of projections such as 30–40 can be sufficient for indexing the grain orientations and resolving the grain shape with a reasonable accuracy; and(iii) for common metals, it is recommended to maximize the electron current by limiting the accelerating voltage to a level of 100–110 kV, and thereby maximizing the photon numbers with energies in the 20–60 keV range.While this study was limited to examining pure iron, some of the results can be generalized to other materials and the method used can be applied to any material. Last but not least, the analysis suggests that the spot overlap rate should also be considered in the reconstruction process or in the evaluation of the reconstructed result.