Rod Bundle Research Articles

Turbulent flow characteristics in an 84-pin rod bundle for typical and damaged spacer grids

Hexagonal rod bundles arranged in a tightly packed triangular lattice are extensively used for heat transfer and energy generation applications. Staggered spacer grids are used to maintain the structural integrity of gas-cooled fast reactor (GFR) fuel assemblies, while inducing localized turbulence in flow. Damage to these spacer grids results in a disruption of flow fields within these hexagonal fuel bundles. Experimental flow visualizations are critical to identify the differences in local flow properties that the structural damage may cause. This experimental research investigates the flow-field characteristics at a near-wall and center plane in a prototypical 84-pin GFR fuel assembly. Newly installed typical spacers and spacers subject to naturally occurring damage due to material degradation over prolonged experimentation were investigated. Velocity fields were acquired by utilizing the matched-index-of-refraction method to obtain time-resolved particle image velocimetry measurements for a Reynolds number of 12 000. Reynolds decomposition statistical results divulged differences in the time-averaged velocity, velocity fluctuations, flow anisotropy, and Reynolds stress distributions. Galilean decomposition demarcated the influence of spacer grid damage on the velocity fields. To extract turbulent structures and elucidate mechanisms of flow instabilities, proper orthogonal decomposition analysis was employed. Reduced order flow reconstructions enabled the application of vortex identification algorithms to determine the spatial and statistical characteristics of vortices generated. This research work provides unique experimental data on the spacer grid condition-dependent flow. The results offer a deeper understanding of fluid dynamics behavior to support GFR rod bundle design efforts and computational fluid dynamics model validation.

Experimental investigation on onset of nucleate boiling and flow boiling heat transfer in a 5 × 5 rod bundle

A flow boiling heat transfer experiment has been carried out in a square arranged 5 × 5 vertical rod bundle. The inlet pressure of the test section ranges from 3.5 to 7 MPa, mass flux varies from 250 to 500 kg/m2·s, heat flux changes from 180 to 200 kW/m2, and the vapor quality is lower than 0.25. The wall superheating degree data at the onset of nucleate boiling (ONB) point and the heat transfer data of both subcooled and saturated flow boiling regions are obtained. Parametric effects on wall superheating degree at ONB point and flow boiling heat transfer coefficient (HTC) are examined. For the present test conditions, an increase in mass flux or system pressure will decrease the wall superheating degree. The HTC in the subcooled and saturated boiling regions is not sensitive to the change of mass flux, while it increases in system pressure. The experimental data also have been compared with the existing empirical correlations. For the wall superheating degree, the existing ONB correlations are all significantly deviated from the experimental data, and a new ONB correlation is proposed to predict the experimental data. For the HTC in the subcooled boiling region, the Shah correlation provides good prediction accuracy for the current experimental data. For the HTC in the saturated boiling region, the selected correlations are all significantly deviated from the experimental data, and a new saturated boiling correlation that has a higher prediction accuracy for present data is established.

A methodology for CHF prediction in VVER rod bundles

The critical heat flux (CHF) is an important thermal–hydraulic parameter that must be determined during the design of water-cooled reactors to ensure safety of operation. In this paper, a methodology is proposed to predict the CHF in VVER11VVER is a transliterated acronym for “vodo-vodyanoi energetichesky reaktor” which literally means “water-water power reactor” (Nuclear Energy Agency, 2021). rod bundles. A whole-reactor model of VVER-1000 is implemented in RELAP-SCDAPSIM, and, based on the bundle-average approach, the parameters of the hot channel are used to assess four CHF predictors (i.e., the 2006 Groeneveld look-up table (LUT), and the Bowring, W-3, Biasi, and OKB-Gidropress correlations) upon comparison with the 2011 Bobkov LUT. A brief critique is given of the correction factors for both the Groeneveld and Bobkov LUTs. The effects of channel diameter and non-uniform axial heat flux on the predicted values of CHF in subcooled conditions are also studied. The performance and time complexity of the standard and Bourke trilinear interpolation algorithms are assessed for use with LUTs in safety codes. It has been concluded that the non-uniform axial heat flux does not affect the CHF in subcooled conditions and that the Groeneveld diameter factor exponent gives better predictability of the CHF in VVER rod bundles over the Tanase and Wong exponent correlations. Additionally, the Groeneveld LUT has been found to nearly reproduces the Bobkov LUT CHF values when used in conjunction with the Bobkov heated length factor. Values of MDNBR equal to 1.83 and 1.96 can be used as thermal limits at 12% overpower when the Bowring and W-3 correlations, respectively, are used in subcooled conditions. The standard and Bourke algorithms nearly exhibit the same average CPU time. The Bourke algorithm, however, is less affected by noise. Further research is needed to ensure the smoothness of the Bobkov LUT and to derive reactor type-dependent correction factor formulas for use with the Groeneveld LUT.

Development of friction factor correlations for hexagonal and square bundles with rough rods based on CFD

Changes in fuel assembly roughness caused by crud deposits can influence the flow resistance characteristics of the fuel assembly. The existing correlations cannot accurately predict the friction factor of the rod bundle with different wall roughness. The friction pressure drop factor of the rod bundle was calculated using the two-equation k-ω shear stress transport (SST) turbulence model to investigate the impact of surface roughness on the friction pressure drop factor of the rod bundle. Two new friction factor correlations are proposed based on the simulation results. The new correlations can accurately predict the pressure drop of the rod bundle in the laminar flow region, the transition region, and the turbulent flow regime. The application ranges of the new correlations are 1.1 < P/D < 1.5, 100 < Re < 700000, and the absolute roughness within 100 μm. The new correlations will be helpful in the design and safety analysis of light water reactors.

Turbulent convective heat transfer behavior of supercritical water flowing upward in 2 × 2 rod bundle channels with various spacers

The turbulent flow and heat transfer characteristics of supercritical water, flowing in vertical 2 × 2 rod bundle channel, are numerically investigated to find useful methods to improve the cooling performance in the core of a supercritical water-cooled reactor. The heat transfer behavior as a function of mass flux and inlet temperature is analyzed and discussed. Standard grid and helical wire spacers are added to the channel, and overall heat transfer performance is evaluated and compared. The results indicate that the fuel rods can be cooled more effectively when the fluid temperature is near the pseudocritical point due to the high specific heat capacity at this temperature and pressure, and the local heat transfer coefficient can be improved greatly from the application of grid spacers; however, heat transfer enhancement only happens in limited regions downstream of the grid spacers. By contrast, strong swirl flow can be induced by a helical wire, thus the mixing of coolant is strengthened, and the convective heat transfer is enhanced. However, local hot spots also occur in the region near the wires. Both grid and helical wire spacers will lead to an increase in pressure loss, but the additional pressure drop induced by the helical wire is smaller, hence better comprehensive heat transfer performance is achieved for a wire-wrapped channel. Moreover, heat transfer performance can also be enhanced by reducing the pitch of the spacers. This suggests that applying spacers and optimizing their configurations and structures is helpful to achieving better cooling performance in rod bundle channels.

Improved Radiation Heat Transfer Model in RELAP5 for Compact Fuel Rod Bundles by the Absorption Factor Modification

Simulations of radiation heat transfer in fuel rod bundles are necessary for the thermal hydraulic design and safety analysis of open lattice gas-cooled reactors, which always operate at high temperatures. To save the computational costs, existing radiation models in system codes such as RELAP5 commonly assume each fuel rod to own the uniform radiosity over the rod surface. Previous research studies have indicated that the uniform radiosity assumption could overestimate the heat transfer flux and under-predict the maximum fuel rod temperature, and the anisotropic correction was tried by dealing with non-uniform reflected radiation. To better model the non-uniform radiosity effect, the Gehart’s method based on the non-uniform absorbed radiation is introduced in this study. By dividing the surface of each rod into six segments, the one-sixth rod view factors are derived in specific rod and near wall sections to generate the segment-to-segment absorption factors. By summarizing those segment-to-segment absorption factors, the rod-to-rod and rod-to-wall absorption factors are modified and implemented into RELAP5 to improve the radiation heat transfer model. The two-dimension radiation heat transfer problem in the nuclear fuel rod bundle is simulated in FLUENT as the benchmark and in RELAP5 for comparison. Fuel rod bundles in hexagonal arrays were investigated with various surface emissivity and pitch-to-diameter ratios (p/d). The simulations indicated that the method of rod segment division and absorption factor modification could reflect the non-uniform radiosity, and the results were related to the values of p/d and surface emissivity. The modified radiation heat transfer model in RELAP5 validated that the deviations of the maximum temperature were reduced from around 20% to 1%,3%,8% for p/d = 1.1, 1.2, and 1.3, respectively. Rod bundles with larger p/d required more radiative rods in the analyses of absorption factor modifications. The present radiation heat transfer model should be studied and tested in three-dimension cases to further prove that it is appropriate for the nuclear rod bundles.

Prediction of reflood behavior in a bundle with deformed and un-deformed rods in ATHER 5 × 5 experiment using MARS-KS code

A reflood experiment at ATHER 5×5 rod bundle facility having an array of deformed rods is calculated using MARS-KS code. In the experiment, the deformed rods were represented by the heater rods with sleeves on the outside. To represent properly the configuration, the sleeve thermal conductors, the steam gap between the heater rod and the sleeve, and the fouling factor into the heat transfer area by contact between adjacent sleeves are implemented. The portion into which the sleeve is installed and the portion not installed are modeled as separate heat structures. Also the heat loss through the housing of the test section is modeled. Within the range of the present calculations, imposing a convective heat transfer coefficient of 2 W/m2·K over the housing can be considered appropriate for the actual heat loss. Calculations are conducted using one-dimensional model with single channel, one with two channels, and three-dimensional model by ‘multid’ component of the MARS-KS code. From the calculation results, the predictability of the code and the present modeling scheme is discussed in terms of overall response, peak cladding temperature, and time of quenching. Sensitivity study on interfacial friction model multiplier is also performed, which shows the quenching time can be improved by applying a multiplier 1.05 to the interface friction model in the one-dimensional case, but its effect on the maximum cladding temperature and the rewet temperature seems not to be significant. The differences in phenomena between the deformed rods and un-deformed rods and their reasons are discussed. The effect of 90% of partial blockage is expected less than 30 K in terms of maximum cladding temperature for both deformed and non-deformed rods, compared to the hypothetical case of the completely un-deformed rod bundle, because cooling can be maintained by flows through the remaining unblocked flow paths.

Simultaneous measurement of the structures of the velocity and thermal boundary layers in the rod bundle channel

The complex geometry of the rod bundle fuel assemblies makes the measurement of velocity and temperature difficult, which hinders the design and optimization of the thermohydraulic performance of the advanced fuel assemblies. In the present study, Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF) techniques are used to simultaneously measure and reconstruct the structures of the velocity and thermal boundary layers. The velocity and temperature distributions near the rod surface under different flow and heat transfer conditions are quantitatively analyzed and compared. The experimental results indicate that increasing the heat flux would increase the near-wall velocity gradient and decrease the temperature gradient. The buoyancy increases with the increase of the heat flux, reducing the turbulent fluctuation in the channel, thereby weakening the generation and diffusion of the turbulent vortex. The dimensionless velocity distribution is obtained by fitting the experimental data to the Spalding formula. Based on the structure of the boundary layer, the increase of buoyancy significantly reduces the proportion of the logarithmic law layer in comparison to the inner layer of the boundary layer. This weakens the convective heat transfer in the channel. The increase of the Reynolds number increases the turbulent fluctuation in the channel and weakens the influence of the buoyancy. Thus, under constant heat flux, the increase of the Reynolds number increases the proportion of the logarithmic law layer in comparison to the inner layer, which enhances the convective heat transfer in the channel.

Sensitivity analysis using improved two-fluid model-based 1D code with the state-of-the-art constitutive equations for two-phase flow in rod bundle

Sensitivity analysis using improved two-fluid model-based 1D code with the state-of-the-art constitutive equations for two-phase flow in rod bundle

The fouling and thermal hydraulic coupling study on the typical 5 × 5 rod bundle in PWRs

The state of the nuclear reactor core is significant, and the corrosion products will be deposited in the core, threatening its safety. In this paper, the analytical model of fouling deposition and migration process is established, and the core corrosion deposition-thermal-hydraulic coupling analysis method is proposed to study the fouling deposition and its effect on the flow and heat transfer state under the long-term operation of the typical 5 × 5 rod bundle channel. The results show that the established model is reasonable. The distribution of fouling in the bundle is related to the position. Under the operating conditions calculated in this paper, the amount of fouling in the outer layer bundle is higher than that in the inner layer. And the fouling rate is positively correlated with the wall temperature. The fouling rate will be greater in the place with higher wall temperature in the bundle. The content of this study could provide reference for the study of reactor core fouling and its heat transfer characteristics.

Experimental investigation of droplet parameters in a 2×2 rod bundle under air-water annular-mist flow

An experimental study was conducted to investigate the local droplet parameters for annular-mist air-water flow in a 2 × 2 rod bundle. It covered a flow condition of a superficial gas velocity (jg) range of 25–35 m/s (gas Reynold number (Reg) range of 39,132–54,785) and a superficial liquid velocity (jl) range of 0.015–0.040 m/s (liquid Reynold number (Rel) range of 432–1153) in an atmospheric pressure. From the test, the distributions of the local droplet parameters such as the droplet fraction, velocity, and diameter were measured by using a double sensor optical fiber probe (OFP). The effect of the superficial gas and liquid velocities on the local droplet parameters have been identified. Furthermore, the droplet mass flux over the measurement cross-section was obtained from the local droplet parameters distributions. It was found that the droplet mass flux has a decreasing trend with the superficial gas velocity and an increasing trend with superficial liquid velocity. That was attributed to the significant effect of the liquid film on the measured droplet mass flux and its trends. Moreover, the present droplet mass flux data were compared with the prediction of three existing droplet entrainment and deposition models. Finally, new entrainment and deposition rate models for predicting the droplet mass flux of a rod bundle were proposed and validated. The applicability of the proposed models is within the present experimental flow conditions range with a mean absolute percentage error (MAPE) of 10.34%.

Numerical investigation of heat exchanger pipe equipped with chamfered circular ring separated from wall to intensify thermo-hydraulic performance

Chamfered circular ring (CCR) innovated from conventional circular ring by introducing chamfered surface on its periphery at 30o attack angle is numerically investigated to study its effect on fluid flow characteristics, heat transfer enhancement, and friction factor in a heat exchanger pipe. In order to study flow blockage effect on overall performance of device, three diameter ratios (DR = Di/Do = 0.6, 0.7 and 0.8) with three spacing ratios (SR = s/D = 1, 2 and 3) are used. Turbulent model k – ε, RNG with enhanced wall treatment is used to solve governing equations. Results showed that CCR chamfered surface produced nozzle jet effect on pipe wall surface through clearance of 1 mm, which further induced turbulent and recirculating flow effect near pipe wall area. This resulted into higher heat transfer rate. All the diameter ratios with SR = 1 showed thermal performance factor value more than unity at most of the lower Reynolds number. The range of TPF shown by DR = 0.6, 0.7 and 0.8 with SR =1 is 1.21–0.93, 1.23–0.97, and 1.19–0.99, respectively. Compromised results of TPF are shown by DR = 0.7 and DR = 0.8 at SR = 1. Chamfered circular ring has shown better results over circular ring, perforated conical ring, short length twisted tape, twin co-twisted tape, wire rod bundles, and perforated twisted tape. Numerical results showed better agreement with predicted results within the range of 10%. Highest TPF of 1.23 is shown by DR = 0.7 and SR = 1 at Re 6000.

Spacer effects on thermal-hydraulic performance of fluid flow at supercritical pressure in annular channel - CFD methodology

Spacer is a vital component in assembly of nuclear fuel rod bundles. It is used to support and maintain suitable distance between the rods in assembly of nuclear fuel bundle. Spacer promotes the local heat transfer in downstream to the spacer in rod bundle. The objective of present work is to analyse the spacer effects on thermal and hydraulic performance of R-134a at supercritical condition of pressure 4.5 MPa in an annular flow. A Computational Fluid Dynamics (CFD) code ANSYS Fluent has been used for present numerical analysis and SST (Shear Stress Transport) k-ω turbulence model was considered for turbulence flow analysis. Numerical analysis was carried out in an annular channel of 6 mm hydraulic diameter with spacer, located at middle of channel. Hydraulic and thermal performance due to the spacer have been investigated for three different mass flow rates (0.33175, 0.41469 and 0.53909 kg/s) and three different heat fluxes (60, 100 and 160 kW/m2 ). Two blockage ratios of 0.3 and 0.38 have been used in present analysis. Due to the presence of spacer as flow obstruction, it is observed that at spacer location, velocity increased significantly and subsequent decrease in pressure. Also; it is noticed that the wall temperature is decreased and corresponding coefficient of heat transfer enhanced significantly at the location of spacer in annular channel. The observed value of ratio of Nusselt number for the case of spacer and without spacer (Nu/Nu*) shows better agreement with correlations data for flow obstacle at Re=97000.

Testing the Modified Subchannel tempa-sc Code in Comparison With Experiments and Other Computer Codes

Abstract The paper describes a modified version of the tempa-sc computer program designed to calculate temperature fields in bundles of rods cooled by a supercritical pressure (SCP) fluid. This version of the program is based on the subchannel method that was used in the tempa-1f program, developed earlier in the OKB “GIDROPRESS” for calculating heat and mass transfer in the core of VVER-type reactors cooled by single-phase water at subcritical pressure. As the relations that close the system of equations of mass, momentum, and energy conservation, the new version of the program includes correlations for calculating heat transfer and friction resistance, taking into account the strong dependence of the properties of the coolant on temperature and pressure. In particular, the use of the universal calculation model of heat transfer, developed by the authors of this paper, allows us to perform calculations in a wide range of flow parameters of various fluids, including the modes of normal, improved and deteriorated heat transfer. The results of tests of the tempa-sc program are presented in comparison with the available experimental data for water and modeling fluids (carbon dioxide, freons R-12 and R-134a) at SCPs, as well as with the published data of calculations by using similar subchannel programs (cobra-sc, assert-pv) and CFD codes. A qualitative agreement between the calculated and experimental data is shown.

Single-phase flow in helical cruciform fuel assembly with conjugate heat transfer

The helical cruciform fuel (HCF) is promising to improve the power density and safety margin of reactors core by its advantages in the heat transfer area-to-volume ratio and continual inter-channel mixing. In this work, the turbulent mixing and heat transfer characteristics of HCF assembly for pressurized water reactor was studied. A novel mesh generation strategy was used to discretize the computational domain of helical fuel assembly with hexahedron meshes. The velocity field, inter-channel cross flow intensity, heat transfer coefficient and the circumferential distribution of wall temperature and heat flux were obtained based on the CFD simulation. The cross flow intensity in the side gaps was greater than that in the internal gaps, which were all significant larger than that of traditional circular rod bundle. The heat transfer coefficient of helical fuel assembly was slightly larger than traditional circular rod bundle under same mass flow rate condition. The helical fuel assembly can offer 38.4% more heat transfer area. The peak-to-average heat flux in the circumferential direction was larger than 2.0, which may result in early boiling crisis.

Numerical investigation of two-component single-phase natural convection and thermal stratification phenomena in a rod bundle with axial heat flux profile

The most numerical investigations of the thermal-hydraulic phenomena following the loss of the residual heat removal capability during the mid-loop operation of the pressurized water reactor were performed according to simplifications and are not sufficiently accurate. To perform more accurate and more reliable predictions of thermal-hydraulic accidents in a nuclear power plant using computational fluid dynamics codes, a more detailed methodology is needed. Modelling results identified that thermal stratification and natural convection are observed. Temperatures of lower monitoring points remain low, while temperatures of upper monitoring points increase over time. The water in the heated region, in the upper unheated region and the pipe region was well mixed due to natural convection, meanwhile, there is no natural convection in the lower unheated region. Water temperature in the pipe region increased after a certain time delay due to circulation of flow induced by natural convection in the heated and upper unheated regions. The modelling results correspond to the experimental data. The developed computational fluid dynamics methodology could be applied for modelling of two-component single/two-phase natural convection and thermal stratification phenomena during the mid-loop operation of the pressurized water reactor or other nuclear and non-nuclear installations at similar conditions.

Numerical investigation on flow-induced vibration and heat transfer of fuel rods in a small pitch-diameter ratio (P/D) channel

The Korea Atomic Energy Research Institute developed a dual-cooled annular fuel rod bundle structure to enhance the core power of the nuclear reactor and improve its heat transfer efficiency. The structure also reduced the pitch-diameter ratio (P/D) of the channel. In this study, a four-subchannel model is taken as the research object, and the Reynolds stress model (RSM) is applied to calculate the flow-solid-thermal tri-physical field coupling for a typical bare rod beam channel. The accuracy of the numerical calculation method used in this study was first verified by comparing it with the experimental data in the literature. Then, the channel flow field under different P/D conditions was simulated, and the formation conditions and influencing factors of the vortex-street structure were studied. Axial flow-induced vibrations of a cylindrical structure in a channel were investigated using a weak coupling algorithm. Finally, the influence of the vortex-street structure on the heat transfer efficiency of the fluid in the channel is discussed. The results show that the anisotropy-based RSM turbulence model can accurately capture the vortex-street structure in small P/D channels. When P/D < 1.050, a stable vortex-street structure appeared in the channel, which led to the stable micro-amplitude vibration of the cylindrical structure in the channel. The presence of the vortex-street structure significantly improves the heat transfer efficiency of the fluid in the channel.

Experimental study of gas-liquid flow patterns and void fraction in prototype 5 × 5 rod bundle channel using wire-mesh sensor

In this paper, the wire-mesh sensor (WMS) has been successfully introduced into a typical pressurized water reactor (PWR) prototype 5 × 5 rod bundle channel. Combined with the high-speed camera, the typical flow patterns and phase distribution of air–water two-phase flow in the rod bundles are experimentally studied. The gas superficial velocity is 0.020 ∼ 1.102 m/s and liquid superficial velocity is 0.041 ∼ 1.604 m/s. The results indicate that the WMS can accurately identify bubble, cap bubble, cap churn and churn flow. Due to the influence of the wall effect, flow patterns between the subchannels of the rod bundle channel are not completely consistent with the global flow pattern. After evaluating the existing drift-flux models, new correlations of distribution parameter and drift velocity for different flow patterns in rod bundle channel are proposed, which shows a good prediction capability.

Validation of the TWOPORFLOW code for the core analysis of liquid metal-cooled reactor with selected experiments

TWOPORFLOW (TPF) is a thermal–hydraulic code that utilizes a porous medium approach in three-dimensional Cartesian coordinates. It can simulate the flow phenomenon in fuel assemblies or reactor cores by solving three conservation equations (single-phase) or six conservation equations in a two-fluid liquid–vapor approach. Many constitutive correlations e.g. pressure loss, interfacial friction, and heat transfer (wall, liquid–vapor interface), are included to close the system of equations. The code was recently extended to simulate pre-Critical Heat Flux (CHF) and CHF heat transfer relevant for Boiling Water Reactor (BWR). In this paper, the code's simulation capability for liquid metal-cooled reactors core is validated using three experimental data sets: pressure drop of the 19-pin rod in THEADES LBE loop, the BREST-type reactor benchmark problem, and the NACIE-UP Block Fuel Pin Simulator (BFPS) test. The results show that TPF can be used not only for square rod bundle arrangements but also for hexagonal arrangements; the code can reasonably predict the thermal–hydraulic behavior of liquid metal-cooled reactors under normal and off-normal conditions.

Flow structures of the cross-flow over a five-layer helically coiled steam generator geometry

The helically-coiled heat exchanger (HCSG) offers advantages over straight tubes such as compactness in geometry, increased heat transfer coefficients, and capability to absorb thermal expansion. In this study, the time-resolved velocity field data of shell-side crossflow over a five-layer helically coiled steam generator geometry was obtained using Particle Image Velocimetry (PIV) between adjacent rods in four regions with up to 5000 frames per second (5 kHz) at approximately Reu = 3600. The slant rod bundle created different flow patterns in different regions. Proper Orthogonal Decomposition (POD) revealed high-energy-mode flow structures. Due to the confined flow channel geometry, the large flow structures were not advected resulting in no strong POD mode paring. Continuous Wavelet Transform (CWT) visualized the characteristics of flow fluctuation in time and frequency domain simultaneously, which ranged in Strouhal number, Su, between 0.03 and 1.17. In the wake regions of the rods, flows changed in both pattern and magnitude over time. Once a pattern formed, it continued for relatively shorter than straight tube arrays, before changing the pattern again. The histograms of the POD time coefficients presented this multimodal flow characteristics. The current study focuses more on whole flow field analyses in the selected regions rather than local point-wise analyses. This study revealed that various Strouhal numbers can exist in the helically coiled heat exchanger geometry, which was not observed in straight tube arrays. In particular, Strouhal numbers smaller than 0.1 do not seem to be caused by vortex shedding but seem to be the result of the combination of complex geometry and possible multimodal trends.Based on the current observation, further works would involve intensive instantaneous point-wise analyses on the interactions between important locations such as separation points, stagnation points, shear layers, etc.