Two-dimensional Experiments Research Articles

Contrast of hydraulic conductivity induces transport of combined pollutants in high- and low-permeability systems

The transport process of pollutants in the environment can be influenced by heterogeneous geologic architecture and pollutant interactions. However, there has been a lack of research on co-transport behaviors of combined pollutants in heterogeneous aquifers. In this study, a series of two-dimensional tank experiments were carried out to study the transport behavior of toluene and naphthalene in both homogeneous and heterogeneous aquifers. The results revealed that the coexisting solutes facilitated the transport of toluene and naphthalene in the homogeneous aquifers, potentially due to competitive adsorption between these compounds. In the high- and low-permeability systems, the transport rates for both toluene and naphthalene decreased while exhibiting characteristics such as early arrival, long tails, and multiple peaks. The spatial analysis of pollutant distribution indicated that hydraulic conductivity contrast played a critical role in inducing back diffusion phenomenon. Furthermore, toluene exhibited more pronounced matrix diffusion compared to naphthalene in heterogeneous aquifers, characterized by higher concentrations, wider diffusion range in low-permeability zones. And the β value for toluene is smaller than naphthalene in CTRW model, indicating that the former is more sensitive to the hydraulic conductivity contrast. This study provides novel insights into understanding the co-transport behavior of combined pollutants in heterogenous aquifers.

Evolution of linear internal waves over large bottom topography in three-layer stratified fluids

Evolutions of internal waves of different modes, particularly mode 1 and mode 2, passing over variable bathymetry are investigated based on a new numerical scheme. The problem is idealized as interfacial waves propagating on two interfaces of a three-layer density stratified fluid system with large-amplitude bottom topography. The Dirichlet-to-Neumann operators are introduced to reduce the spatial dimension by one and to adapt the three-layer system and significant topographic effects. However, for simplicity, nonlinear interactions between interfaces are neglected. Numerical techniques such as the Galerkin approximation, proven effective in previous works, are applied to save computational costs. Shoaling of linear waves on an uneven bottom is first studied to validate the proposed formulation and the corresponding numerical scheme. Then, for two-dimensional numerical experiments, mode transition phenomena excited by locally confined bottom obstacles and quickly varying topographies, including the Bragg resonance, mode-2 excitation, wave homogenization, etc., are investigated. In three-dimensional simulations, internal wave refraction by a Luneberg lens is considered, and good agreement is found in comparison with the ray theory. Finally, in the limiting case, when the top layer can be negligible (for example, a gas layer of extremely small density), the problem is reduced to a two-and-a-half-layer fluid system, where an interface and a surface are unknown free boundaries. In this situation, the surface signature of an internal wave is simulated and verified by introducing the realistic bathymetry of the Strait of Gibraltar and qualitatively compared with the satellite image.

Deciphering Spectroscopic Signatures of Competing Ca2+ - Peptide Interactions.

Calcium-protein interactions are of paramount importance in biochemistry. They are a key element in a number of biological processes, such as neuronal signaling. Therefore, an understanding of the interaction at the molecular level is highly desirable. Here, we study the zwitterionic model peptide l-alanyl-l-alanine (2Ala), which has two distinct and competing binding sites for Ca2+: The carbonyl of the peptide bond and the C-terminus, the carboxylate group. We perform linear and two-dimensional IR spectroscopy experiments and find that the spectroscopic signatures of both moieties in the IR spectra change in amplitude and peak position upon the addition of CaCl2: A blueshift of the asymmetric carboxylate band and a redshift for the amide I mode. Ab initio molecular dynamics simulations confirm the direct interaction of the Ca2+ ion at both the carboxylate and the amide CO site leading to different spectral responses. The blueshift of the asymmetric carboxylate band is caused by a localization of the charge, leading to a decoupling of the CO stretching modes of the carboxylate group. The slight redshift of the amide I mode of 2Ala upon the addition of CaCl2 contrasts the blueshift that has been observed for isolated amide motifs, such as N-methylacetamide (NMA). This difference is caused by the smaller number of water molecules being replaced by the Ca2+ ion for 2Ala's amide compared to less sterically hindered, isolated amide carbonyls, in conjunction with vibrational Stark effects. Our results highlight the importance of considering potential competing binding sites, such as the amide CO backbone, the termini and residues, as well as the nature of the hydration of both peptide and ion, when exploring ions' interacting with small peptides and larger proteins.

NMR-Based Stable Isotope Tracing of Cancer Metabolism.

NMR is widely used for metabolite profiling (metabolomics, metabonomics) particularly of various readily obtainable biofluids such as plasma and urine. It is especially valuable for stable isotope tracer studies to track metabolic pathways under control or perturbed conditions in a wide range of cell models as well as animal models and human subjects. NMR has unique properties for utilizing stable isotopes to edit or simplify otherwise complex spectra acquired in vitro and in vivo, while quantifying the level of enrichment at specific atomic positions in various metabolites (i.e., isotopomer distribution analysis).In this protocol, we give an overview with specific protocols for NMR-based stable isotope-resolved metabolomics, or SIRM, with a workflow from administration of isotope-enriched precursors, via sample preparation through to NMR data collection and reduction. We focus on indirect detection of common NMR-active stable isotopes including 13C, 15N, 31P, and 2H, using a variety of 1H-based two-dimensional experiments. We also include the application and analyses of multiplex tracer experiments.

Two-Dimensional Physical Model Experimental Study on Sweep Efficiency of Offshore Heavy Oil Hot Water Flooding

Abstract The conventional water flooding approach for the development of ordinary heavy oil faces challenges such as high injection-production mobility, rapid increase in water cut, and low final recovery. By using the temperature-sensitive properties of heavy oil, the viscosity can be effectively reduced, and the flow capacity within porous media can be enhanced by increasing the temperature of injected water. Onshore hot water flooding is primarily used to exploit the remaining oil potential during the later stages of steam stimulation, while offshore is used to enhance efficiency during the mid to late stages of water flooding. The key to the success of hot water flooding technology lies in the improvement of the sweep coefficient. Firstly, a two-dimensional physical experiment model is designed in accordance with the geological and reservoir characteristics of the target oilfield, based on the principle of similarity. Secondly, parameters that quantitatively characterize the development law of the plane temperature field, such as the effective sweep coefficient, regular factor, and plane expansion speed of the high-temperature region, are studied. Then, through two-dimensional experiments, the effects of injection medium, formation rhythm, and timing of hot water injection on sweep efficiency and temperature field development were discussed. Finally, on the basis of two-dimensional experiments, the effects of heat injection temperature, timing of heat injection, hot water injection speed, and high permeability strip on the improvement of sweep efficiency were quantitatively analyzed by numerical simulation. The results show that compared with hot water flooding, hot water composite flooding can increase the effective sweep coefficient from 15.05 % to 28.71 %. The anti-rhythm is helpful to the upward expansion of the high temperature zone, which can increase the oil displacement efficiency by 1.5 %. Water channeling can be effectively controlled by injecting hot water with low water cut. The increase of heat injection temperature is helpful to increase the proportion of high temperature heating area. The higher the injection speed, the greater the expansion speed of the heating chamber. The research results provide a direction for the development of heavy oil conventional water flooding to improve oil recovery in offshore heavy oil.

Two-dimensional distribution experiment of ‘lattice diffraction’ using ultrasound in an educational laboratory

Abstract A device that can study the two-dimensional distribution of ultrasonic diffraction on lattice structures was developed for educational laboratories, enabling students to design the size, shape and dimension of diffraction obstacles independently. In this experiment, metal balls were used to simulate atomic lattice structures, and the two-dimensional diffraction distribution data of simple cubic, body-centered cubic, and hexagonal close-packed structure were collected. The results were compared with the sound field simulation of COMSOL, and a good consistency was found. By observing the diffraction results of complex structures, students can gain a better understanding of the concept of diffraction.

Adaptive Variational Quantum Computing Approaches for Green's Functions and Nonlinear Susceptibilities.

We present and benchmark quantum computing approaches for calculating real-time single-particle Green's functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation. Using automatically generated compact circuits, the dynamical evolution is performed over sufficiently long times to achieve adequate frequency resolution of the response functions. We showcase accurate Green's function calculations using a statevector simulator on classical hardware for Fermi-Hubbard chains of 4 and 6 sites, with maximal ansatz circuit depths of 65 and 424 layers, respectively, and for the molecule LiH with a maximal ansatz circuit depth of 81 layers. Additionally, we consider an antiferromagnetic quantum spin-1 model that incorporates the Dzyaloshinskii-Moriya interaction to illustrate calculations of the third-order nonlinear susceptibilities, which can be measured in two-dimensional coherent spectroscopy experiments. These results demonstrate that real-time approaches using adaptive parametrized circuits to evaluate linear and nonlinear response functions can be feasible with near-term quantum processors.

Pore-Scale Mechanism Analysis of Enhanced Oil Recovery by Horizontal Well, Dissolver, Nitrogen, and Steam Combined Flooding in Reducer Systems with Different Viscosities for Heavy Oil Thermal Recovery

Horizontal well, dissolver, nitrogen, and steam (HDNS) combined flooding is mainly applied to shallow and thin heavy oil reservoirs to enhance oil recovery. Due to the lack of pore-scale mechanism studies, it is impossible to clarify the oil displacement mechanism of each slug in the process combination and the influence of their interaction on enhanced oil recovery (EOR). Therefore, in this study, HDNS combined flooding technology was simulated in a two-dimensional visualization microscopic model, and three viscosity reducer systems and multi-cycle combined flooding processes were considered. In combination with an emulsification and viscosity reduction experiment, two-dimensional microscopic multiphase seepage experiments were carried out to compare the dynamic seepage law and microscopic occurrence state of multiphase fluids in different systems. The results showed that the ability of three viscosity reducers to improve viscosity reduction efficiency in HDNS combined flooding was A > B > C, and their contributions to the recovery reached 65%, 41%, and 30%, respectively. In the system where a high viscosity reduction efficiency was shown by the viscosity reducer, the enhancements of both sweeping efficiency and displacement efficiency were primarily influenced by the viscosity reducer flooding. Steam flooding collaborated to improve displacement efficiency. The thermal insulation characteristics of N2 flooding may not provide a gain effect. In the system where a low viscosity reduction efficiency was shown by the viscosity reducer, the steam flooding was more important, contributing to 57% of the sweeping efficiency. Nitrogen was helpful for expanding the sweep area of the subsequent steam and viscosity reducer, and the gain effect of the thermal insulation steam chamber significantly improved the displacement efficiency of the subsequent steam flooding by 25%. The interaction of each slug in HDNS combined flooding resulted in the additive effect of increasing production. In actual production, it is necessary to optimize the process and screen the viscosity reducer according to the actual conditions of the reservoir and the characteristics of different viscosity reducers.

Efficient finite element strategy using enhanced high-order and second-derivative-free variants of Newton's method

In this work, we propose a stable finite element approximation by extending higher-order Newton's method to the multidimensional case for solving nonlinear systems of partial differential equations. This approach relies solely on the evaluation of Jacobian matrices and residuals, eliminating the need for computing higher-order derivatives. Achieving third and fifth-order convergence, it ensures stability and allows for significantly larger time steps compared to explicit methods. We thoroughly address accuracy and convergence, focusing on the singular p-Laplacian problem and the time-dependent lid-driven cavity benchmark. A globalized variant incorporating a continuation technique is employed to effectively handle high Reynolds number regimes. Through two-dimensional and three-dimensional numerical experiments, we demonstrate that the improved cubically convergent variant outperforms others, leading to substantial computational savings, notably halving the computational cost for the lid-driven cavity test at large Reynolds numbers.

Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model

For nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property (ensuring bounded linearized strains even under high stresses). Such strain-limiting Cosserat model can find potential applications in solids and biological fibers. However, Cosserat media with naturally rotational degrees of freedom, nonlinear constitutive relations, high contrast, and heterogeneities may produce challenging multiscale characteristics in the solution, and upscaling by multiscale methods is necessary. Therefore, we utilize the offline and residual-based online (adaptive or uniform) GMsFEM in this context while handling the nonlinearity by Picard iteration. Through various two-dimensional experiments (for perforated, composite, and stochastically heterogeneous media with small and big strain-limiting parameters), our numerical results show the approaches' convergence, efficiency, and robustness. In addition, these results demonstrate that such approaches provide good accuracy, the online GMsFEM gives more accurate solutions than the offline one, and the online adaptive strategy has similar accuracy to the uniform one but with fewer degrees of freedom.

Replicating Visuo-Motor Remapping in the Laparoscopic Environment

Laparoscopy, a minimally invasive surgical technique, requires precise visuo-motor coordination. Because the surgical field is viewed through a camera which may need to be placed to one side of the would-be direct line of sight, rotational distortion is a concern. This study investigates adaptation to rotational distortions by replicating previous computerized two-dimensional perceptual-motor experiments, and measurement methods, using a non-virtual low-fidelity laparoscopic training simulator. This replication was chosen for the opportunity to observe the best-established adaptation mechanisms (gradual and axis-inversion) and carryover effects. To our knowledge, this is the first time that circular statistics are used to analyze directional error data collected in the laparoscopic environment. Results strongly indicated that gradual adaptation occurs with distortions below 90°, and there is leading evidence that axis-inversion occurs in distortions above 90°. This confirms previous observations of task performance decrement in the laparoscopic environment and provides clarification for new research directions.

Structure, Dynamics, and Reactivity of Encapsulated Molecules in Restricted Spaces: Arylazoisoxazoles within an Octa Acid Capsule.

In this study, a well-defined organic capsule assembled from two octa acid (OA) molecules acting as host and select arylazoisoxazoles (AAIO) acting as guests were employed to demonstrate that confined molecules have restricted freedom that translates into reaction selectivity in both ground and excited states. The behavior of these AAIO guests in confined capsules was found to be different from that found in both crystals, where there is very little freedom, and in isotropic solvents, where there is complete freedom. Through one-dimensional (1D) and two-dimensional (2D) 1H NMR spectroscopic experiments, we have established a relationship between structure, dynamics and reactivity of molecules confined in an OA capsule. Introduction of CF3 and CH3 substitution at the 4-position of the aryl group of AAIO reveals that in addition to space confinement, weak interactions between the guest and the OA capsule control the dynamics and reactivity of guest molecules. 1H NMR studies revealed that there is a temperature-dependence to guest molecules tumbling (180° rotation along the capsular short axis) within an OA capsule. While 1H NMR points to the occurrence of tumbling motion, MD simulations and simulation of the temperature-dependent NMR signals provide an insight into the mechanism of tumbling within OA capsules. Thermal and photochemical isomerization of AAIO were found to occur within an OA capsule just as in organic solvents. The observed selectivity noted during thermal and photo induced isomerization of OA encapsulated AAIOs can be qualitatively understood in terms of the well-known concepts due to Bell-Evans-Polanyi (BEP principle), Hammond and Zimmerman.

Study on the mechanism of soil erosion by submerged water jet vertical scouring in cohesive soils

The water jet trenching technique is widely used in the burial of submarine pipelines. However, its application in cohesive soils often leads to complexity in trench morphology and challenges in predicting trench dimensions due to unclear soil erosion mechanisms. These issues significantly impact pipeline burials. To investigate the soil erosion mechanism of water jet trenching in cohesive soils, two-dimensional physical simulation experiments of submerged vertical water jet erosion were conducted. The influence of jet pressure, impingement height, and nozzle diameter on the shape of the scour hole was analyzed. The erosion damage patterns of water jets on cohesive soils were studied, and a theoretical model for the development of scour holes was established. The study revealed that when the jet velocity reaches 1000 m/s and the nozzle diameter reaches 1 mm, a contracted neck forms at the upper part of the scour hole. The appearance of the contracted neck is due to excessive jet impact energy causing impact shear failure in the soil. The effective height and width of the contracted neck increase with jet pressure and nozzle diameter and decrease with impingement height. Based on Prandtl's bearing capacity model, a model for predicting impact shear failure in cohesive soils was established, and a predictive formula for the effective height and diameter of the neck was proposed. Experimental validation confirmed the accuracy of the predictive formula. These findings provide theoretical support for the application of water jet trenching techniques in cohesive seabed soils.

Preliminary Validation of Persulfate Delivery Through Porous Pipe in the Vadose Zone: A Two-Dimensional Sandbox Experiment

ABSTRACT When remediating contamination in the vadose zone, which is a potential source of continuous groundwater and surface water pollution, technical challenges are often encountered. In this study, the feasibility of delivering sodium persulfate (SPS) oxidant to unsaturated soils was explored by integrating porous pipes, commonly used in agriculture, with in-situ chemical oxidation (ISCO). An evaluation of the operating characteristics of the pipe determined a recommended influent rate of < 0.1 L min−1 and an initial influent water pressure < 20 kPa to prevent percolation pore enlargement. Two-dimensional sandbox experiments revealed that pulse infiltration at an influent rate of 0.05 L min−1 was effective in creating matrix flow and lateral movement, minimizing preferential flow induced by continuous infiltration. Application of SPS (10% by wt.) under these conditions resulted in approximately 90% wetting of the sandbox area SPS flow at the experimental time that infiltrated from the pipe. After a 14-d post infiltration resting state, residual SPS concentrations ranged from 6,000 -12,000 mg/kg in soil, with soil pH levels of 3–4, ORP around 600 mV, and 40–60% decreases in soil organic carbon. This developed method helps retain the oxidant and promote chemical reactions, making ISCO a viable option for remediating unsaturated soil contamination.

Investigation of the Dewatering Process with Geotextile Tubes by Sedimentation, One- and Two-Dimensional Filtration Test Methods

AbstractDewatering applications are carried out with geotextile tubes for the disposal or reuse of industrial wastes with high water content. Class F Seyitomer thermal power plant fly ash, an industrial waste, was selected in this study. Turbidity, sedimentation and filtration experiments were carried out using anionic and cationic polymers and polypropylene synthetic fiber to investigate the effect of polymers and fibers on the dewatering of fly ash. The use of polymers was determined to significantly accelerate filtration and soil sedimentation speed while leading to a slight increase in the volume of the filter cake. When effective polymer and dosage are used, slurry filtration time can be reduced up to one-eighth of the time and dewatering can be achieved much faster. The addition of synthetic fiber accelerated the sedimentation of the slurry and increased the filtration in the vertical direction, while it did not show a significant effect on the total filtration in two-dimensional filtration. In geotextile tube applications, although one-dimensional filtration experiments might give misleading results in terms of estimating the effectiveness of the polymers used in solid–liquid separation and dewatering times, the jar test, sedimentation and two-dimensional filtration experiments were determined to give compatible and more realistic results. In two-dimensional filtration experiments, approximately 75% of the filtration occurred in the radial direction and the dewatering time was approximately 21–55% of the time estimated by one-dimensional filtration experiment. Geotextile tube dewatering design can be made more predictable and cost-effective in the field by performing small-scale laboratory experiments with the two-dimensional filtration test system designed for this study and various dewatering applications.

Effect of impeller rotational phase on the FDA blood pump velocity fields.

The Food and Drug Administration (FDA) blood pump is an open-source benchmark cardiovascular device introduced for validating computational and experimental performance analysis tools. The time-resolved velocity field for the whole impeller has not been established, as is undertaken in this particle image velocimetry (PIV) study. The level of instantaneous velocity fluctuations is important, to assess the flow-induced rotor vibrations which may contribute to the total blood damage. To document these factors, time-resolved two-dimensional PIV experiments were performed that were precisely phase-locked with the impeller rotation angle. The velocity fields in the impeller and in the volute conformed with the previous single blade passage experiments of literature. Depending on the impeller orientation, present experiments showed that volute outlet nozzle flow can fluctuate up to 34% during impeller rotation, with a maximum standard experimental uncertainty of 2.2%. Likewise, the flow fields in each impeller passage also altered in average 33.5%. Considerably different vortex patterns were observed for different blade passages, with the largest vortical structures reaching an average core radii of 7 mm. The constant volute area employed in the FDA pump design contributes to the observed velocity imbalance, as illustrated in our velocity measurements. By introducing the impeller orientation parameter for the nozzle flow, this study considers the possible uncertainties influencing pump flow. Expanding the available literature data, analysis of inter-blade relative velocity fields is provided here for the first-time to the best of our knowledge. Consequently, our research fills a critical knowledge gap in the understanding of the flow dynamics of an important benchmark cardiovascular device. This study prompts the need for improved hydrodynamic designs and optimized devices to be used as benchmark test devices, to build more confidence and safety in future ventricular assist device performance assessment studies.

Interactions and pattern formation in a macroscopic magnetocapillary SALR system of mermaid cereal

When particles are deposited at a fluid interface they tend to aggregate by capillary attraction to minimize the overall potential energy of the system. In this work, we embed floating millimetric disks with permanent magnets to introduce a competing repulsion effect and study their pattern formation in equilibrium. The pairwise energy landscape of two disks is described by a short-range attraction and long-range repulsion (SALR) interaction potential, previously documented in a number of microscopic condensed matter systems. Such competing interactions enable a variety of pairwise equilibrium states, including the possibility of a local minimum energy corresponding to a finite disk spacing. Two-dimensional (2D) experiments and simulations in confined geometries demonstrate that as the areal packing fraction is increased, the dilute repulsion-dominated lattice state becomes unstable to the spontaneous formation of localized clusters, which eventually merge into a system-spanning striped pattern. Finally, we demonstrate that the equilibrium pattern can be externally manipulated by the application of a supplemental vertical magnetic force that remotely enhances the effective capillary attraction.

CFD Calculation of Natural Convection Heat Transmission in a Three-Dimensional Pool with Hemispherical Lower Head

The integrity of a pressure vessel (PRV) is affected by the decay heat of the molten pool in the lower head, so it is very important to study the natural convection heat transmission in the lower head. Scholars from all over the world have carried out a lot of experimental studies and calculations to determine the convection mechanism and heat transmission characteristics of the molten pool. Most of them were based on the empirical formula of convective heat transmission on the wall of a hemispherical molten pool based on two-dimensional slice experiments and simulation calculations. In this study, FLUENT 2021R1 software was used to simulate the three-dimensional convective heat transmission process of the hemispherical molten pool, and the temperature, velocity and wall heat transmission coefficients of the flow field were analyzed. The results were in good agreement with experimental data from UCLA (University of California, Los Angeles). Through research on the heat transmission of the lower head, the results showed that in the region where the wall angle was θ between approximately 72 and 90 degrees, heat transmission coefficients had larger fluctuations, and a more reasonable empirical relation was proposed. Comparing between the simulation results of CFD and the two-dimensional empirical formula, it was found that the latter one was smaller under the same θ angle condition. Finally, the convection phenomena of different external temperatures were simulated, and the main factors affecting the flow field by temperature were analyzed.

Efficient dimension-by-dimension adaptive TENO-based limiter and troubled-cell indicator for nodal-based high-order spectral difference method

A new targeted essentially non-oscillatory (TENO) limiter with adaptive dissipation has been developed for the 3rd- and 4th-order spectral difference method. This limiter can potentially be useful for other nodal-based discontinuous high-order methods as well. Unlike traditional WENO limiters for these methods which limit low-order moments one by one, the new limiter is based on a direct convex combination of reconstruction polynomial candidates. This strategy ensures the good computational efficiency for high order reconstructions. The reconstruction stencils only involve nodal values from the target cell and its neighbors sharing faces with it. The reconstruction employs Hermite polynomials, making the new limiter compact. It can be implemented in a dimension-by-dimension manner for multi-dimensional problems, which is consistent with the spectral difference method. To further enhance efficiency, a TENO-based troubled-cell indicator is also developed to only activate limiters in troubled cells. Extensive one-dimensional and two-dimensional numerical experiments validate the performance of the new TENO-based limiter and indicator. In summary, the limiter is much less dissipative than WENO limiters and can resolve richer small-scale flow structures on coarse meshes. The indicator precisely marks out troubled cells, slightly improving over the KXRCF indicator.

Effects of gas-pore sizes and locations on fatigue failure: A peridynamic study

Due to complicated features of gas-pores and great dispersions of fatigue lifetimes in additively manufactured metals, it is cumbersome to reveal the exact effects of gas-pores on fatigue failure by purely analyzing experiment data. In this paper, two-dimensional peridynamic virtual fatigue experiments (PD-VFE) are performed to investigate the effects of a singular circular gas-pore on the fatigue failure in smooth specimens. PD-VFE well captures three different modes of fatigue crack initiation (FCI), which are revealed to dominate the gas-pore impacts on fatigue lifetimes. Effects of two typical features of gas-pores, i.e. locations and sizes, are also clarified; to be specific, gas-pore location is the major factor to decide FCI mode and subsurface gas-pore is the most dangerous, while the role of gas-pore size is to scale the impacts of gas-pore location on fatigue lifetimes. The above PD-VFE results accord with experiment data in variation tendency, and can also explain assumptions and simplifications in Murakami approach.