Small Ratio Research Articles

Rigorous justification of the hydrostatic approximation limit of viscous compressible flows

This paper considers the asymptotic limit of small aspect ratio between vertical and horizontal spatial scales for viscous isothermal compressible flows. In particular, it is observed that fast vertical acoustic waves arise and induce an averaging mechanism of the density in the vertical variable, which at the limit leads to the hydrostatic approximation of compressible flows, i.e., the compressible primitive equations of atmospheric dynamics. We justify the hydrostatic approximation for general as well as “well-prepared” initial data. The initial data is called well-prepared when it is close to the hydrostatic balance in a strong topology. Moreover, the convergence rate is calculated in the well-prepared initial data case in terms of the aspect ratio, as the latter goes to zero.

Obesity and Sex as Determinants of Atherogenic Risk Associated with High-Density (HDL) and Low-Density Lipoprotein (LDL) Subfractions in Adolescents: A Population-based Study Based on Health Survey of Sao Paulo

Background: Worldwide, obesity in adolescents is an epidemiological concern. Overweight and obesity are associated with comorbidities in adult life, such as increased risk of hypertension and other non-communicable diseases. This study investigated possible differences between traditional lipid markers and Low-Density Lipoprotein (LDL) and High-Density Lipoprotein (HDL) subfractions in a population-wide representative sample of Brazilian adolescents. Methods: The individuals included in the study comprise a subsample of the 2015 Health Survey of São Paulo (ISA-Capital 2015). LDL and HDL particle sizes were determined by the Lipoprint® System (Quantimetrix Corporation). Results: 272 Brazilian adolescents with a mean age of 15.2 ± 2.2 years, of which 47.8% (n = 130) are boys. Analysis of LDL subfractions showed an increase in LDL 2 content in girls (5.7% vs. 5.1%; p = 0.047). This result was associated with a higher content of large LDL in girls (17.8% vs. 13.5%; p < 0.001) and a significant, lower content of small LDL (1.7% vs. 3.4%; p = 0.002). When obesity was considered, we observed that regardless of being overweight, girls had higher large and small LDL than boys. However, when a large to small LDL ratio was calculated, girls with no excess weight had higher values than boys with no excess weight (10.6 vs. 9.3; p = 0.038), and these had lower LDL ratio than overweight boys (9.3 vs. 13.5; p = 0.016). On the other hand, boys had higher HDL 2 content than girls (8.9% vs. 8.0%; p = 0.017), which was associated with increased large HDL values in boys (1.9% vs. 1.7%; p = 0.047). Regression analysis was performed according to gender, the sum of very low-density lipoprotein (VLDL) + intermediate density lipoprotein (IDL) C + IDL B subfractions was adjusted for age and body mass index (BMI), showing that girls had lower atherogenic lipid profile (β = 0.987; CI = 0.977-0.998; p = 0.017) than boys. When the regression analysis was performed according to BMI, large LDL in adolescents with no excess weight presented a lower atherogenic lipid profile (β = 1.040; CI = 1.000-1.082; p = 0.049), adjusted for age and sex, than overweight adolescents. Conclusion: Regardless of excess weight, girls showed a cardioprotective profile more associated with a favorable distribution of LDL subfractions than boys, reinforcing the relevance of evaluating qualitative aspects of lipoproteins in addition to the traditional cholesterol content.

125 Effects of Saccharmyces yeast postbiotics on nursey pig muscle fiber cross-sectional area and oxidative capacity

Abstract This study aimed to determine effects of dietary supplementation of Saccharomyces yeast postbiotics (celluTEIN, Puretein Bioscience, LLC, Minneapolis, MN) on nursery pig muscle fiber cross-sectional area (CSA), isoform, and succinate dehydrogenase (SDH) staining intensity. Newly weaned pigs [n = 32; 16 barrows and 16 gilts; 21 d of age, body weight (BW) 6.05 ± 0.24 kg] were stratified by BW within sex, placed in individual pens, and randomly assigned to one of two dietary treatments within each two-pig strata. Dietary treatments included pigs supplemented 0 (CON; n = 16) or 175 g/ton (CT; n = 16) of celluTEIN to their standard three-phase nursery ration. Pigs were harvested at d 35 of feeding and the longissimus lumborum muscle was collected for mean SDH staining intensity and immunohistochemistry analyses. Data were analyzed as a completely randomized design with pig as the experimental unit and treatment as the fixed effect. Statistical significance was determined at P ≤ 0.05. There were no treatment effects on type I and type IIB muscle fiber CSA (P > 0.14), but CT pigs had greater type IIA and type IIX muscle fiber CSA compared with CON (P < 0.05). When not analyzed by fiber isoform, pigs fed CT had a greater (P = 0.02) average muscle fiber CSA than CON pigs. There were no treatment effects on muscle fiber type percentage or SDH intensity of all fiber types (P ≥ 0.23); however, when calculated as a muscle fiber CSA ratio, CT type IIA fibers had a smaller ratio (darker staining/µm2) than CON type IIA fibers (P = 0.05). There were no treatment effects for type I, IIX, and IIB ratios (P > 0.21). In conclusion, supplementing Saccharomyces yeast postbiotics during the nursery period increased muscle fiber hypertrophy and type IIA fiber oxidative capacity.

Parametric analysis on the acoustic characteristics generated by a biomimetic swimmer

Previous studies have shown the excellent hydrodynamic performance of fish swimming. However, the main factors that lead to the low-noise propulsion of fish are still unrevealed. In this study, numerical studies on the characteristics of the far-field sound generated by a bio-inspired swimmer were carried out. The model was simplified as a two-dimension (2D) foil based on the numerous analyses in the past decades. The effects of propulsion methods, model thickness, Strouhal number St, and Reynolds number Re on the flow-induced sound were analysed. Reynolds-Averaged Navier–Stokes (RANS) and Ffowcs Williams–Hawkings (FW–H) equations were employed to simulate the fluid field and the acoustic characteristics, respectively. Simulation results indicated that the sound distribution generated by the biomimetic swimmer exhibits a dipole-like pattern. It was noted that by analysing the effect of motion wavelength on the effective sound pressure, an anguilliform swimmer generates lower sound during propulsion than swimmers with other types of motions. With a small thickness-length ratio, the bio-inspired swimmer could generate large thrust but small sound. Meanwhile, the maximum effective sound pressure is related to the effective lift of the foil.

Analyzing the Factors of Vacant Home Occurrence for Urban Sustainability: A Case Study of Medium-Sized Cities Focusing on Asan City, Chungcheongnam-do

This study aims to enhance urban sustainability by analyzing the spatial distribution and underlying causes of vacant homes in Asan, Chungcheongnam-do. Various statistical methods were employed to analyze date concerning the number of vacant stores, population changes, land use complexity, and the physical characteristics of land and buildings; these factors were found to influence the prevalence of vacant homes across Asan. Additionally, it was found that distinct factors differentially affect specific regions, such as old downtown areas versus rural villages. This indicates that reducing vacant homes in these areas requires distinct policies tailored to the unique circumstances of each region. For instance, in old town areas, small lot ratios and land use complexity are significant, while in rural villages, the average number of floors and land use complexity play a major role. This study highlights the diverse factors influencing the prevalence of vacant homes and suggests that to effectively address this issue, policies should be developed that are tailored to the unique characteristics of each area, categorized at both the city and local levels.

Seismic behavior of precast segmental bridge columns confined by grouted glass fiber reinforced plastic tubes

The application of precast segmental bridge columns (PSBCs) is still restricted in seismicity areas due to concerns such as lower lateral stiffness and column base bearing capacity. To enhance the applicability of PSBCs, this study proposed a novel approach of confining them with grouted GFRP tubes. Four novel and one reference specimens were tested under low cyclic loading to evaluate the effects of energy dissipation (ED) bars ratios, concrete interlayer strength, type of segment concrete, and concrete pouring methods within the outer GFRP tube (OGT) on the seismic behavior. Experimental results reveal that the failure modes of all specimens were triggered by the yielding of ED bars and the break of OGT at the top of ED bars. No crushed concrete at column bases or cracks at the segment joint were observed during the test due to the good confinement of GFRP tubes. All the specimens exhibited stable hysteretic behavior with small residual drift ratios and low strength degradation. Furthermore, finite element models (FEMs) were generated to predict the hysteretic behavior of novel specimens. The effects of some parameters such as OGT thickness, ED bars diameter, and concrete strength were further studied.

Three-dimensional information measurement and reconstruction for micro-hole array based on the modified shape from focus

The geometrical characteristics of the micro-holes and the consistency of spatial distribution among the micro-holes in the micro-hole array fabricated by laser beam drilling (LBD) directly influence the cooling performance, reliability, and longevity of the workpiece. It is of great significance to establish the relationship between the LBD processing parameters and the characteristics of the micro-hole array through the three-dimensional (3D) information measurement and reconstruction of the micro-hole array, as well as to guide and improve the LBD processing technology. However, due to the small size and high aspect ratio of the micro-holes in the micro-hole array, the 3D information measurement and reconstruction of the micro-hole array face challenges. The conventional micro-hole measurement methods suffer from low efficiency, high measurement costs, and potentially destructive measurement processes. Furthermore, the conventional micro-hole measurement methods face challenges in simultaneously obtaining the geometrical characteristics of the micro-holes and the spatial distribution among the micro-holes in the micro-hole array. Therefore, a non-contact and non-destructive 3D information measurement and reconstruction method for the micro-hole array based on the modified shape from focus is proposed. A novel focus measure operator based on grayscale difference and adaptive neighborhood size is proposed to accurately evaluate the focus value and obtain the initial focus volume matrix. A novel image processing operator based on the gradient information of the image sequence is proposed to enhance the initial focus volume matrix. The experimental results indicate that the proposed focus measure operator, combined with the novel image processing operator, is more suitable and reliable for detecting the micro-holes due to its better unimodality, higher contrast, and narrower peak width than the conventional focus measure operator. The optimal focus position of each image point is obtained using the modified Gaussian curve fitting method. On this basis, the 3D information measurement and reconstruction of the micro-hole array are realized. By comparing the results with the conventional micro-hole measurement method, the feasibility and accuracy of the proposed method have been confirmed to be an effective measurement method for the micro-hole array.

Analyze as randomized—Why dropping block effects in designed experiments is a bad idea

AbstractAgricultural experiments are often laid out as blocked designs such as the randomized complete block designs (RCBD) or split‐plot designs (SPD). Statistical analysis should follow the principle “analyze as randomized.” However, block effects are often not modeled or are typically dropped from the model when non‐significant. Additionally, if linear mixed models are fitted by REML with a non‐negativity constraint on all variances, an implicit model reduction occurs when the variance estimate for random block effects becomes negative in the final iteration. This study investigates the consequences of these types of model reduction on the Type I error rate and the standard error of a treatment difference (s.e.d.) by Monte Carlo simulation for experiments designed as RCBD or SPD. The number of blocks and treatments and the ratio of block or main‐plot error variance to residual error variance were varied, resulting in 27 scenarios. Dropping the block effect by default resulted in deflated Type I error rates and increased the s.e.d. in the RCBD. For the SPD, Type I error rates were inflated for the sub‐plot factor and the main‐plot‐by‐sub‐plot factor interaction, but were deflated for the main‐plot factor. Adverse effects of model reduction were reduced, but did not vanish completely, for model reduction based on significance testing. Implicit model reduction led to inflated Type I error rates for small variance ratios and small datasets. We conclude that block effects as well as main‐plot error effects need to be included by all means in statistical analysis.

Viscoplastic flows in channels with small aspect ratio: Bingham versus regularised models

We investigate the two-dimensional flows of a viscoplastic fluid in symmetric channels with impermeable walls under no-slip boundary conditions. To characterise the mechanical response of the viscoplastic fluid we consider both the celebrated Bingham model and a very general class of its regularisations. In order to make the problem amenable to analysis, we assume that the aspect ratio of the channel is small so that the lubrication approximation can be used. This allows us to obtain analytical solutions, perform an asymptotic analysis of the regularised solutions and compare the results predicted by the Bingham model and its regularisations. We find that in the limit as the regularisation parameter tends to zero, the regularised flow tends to those predicted by the Bingham model only in plane channels. In channels with curved walls, the results are instead markedly different.

Investigation on laminated steel slit shear walls with low yield steel

To improve the energy dissipation capacity of steel slit shear walls made of thin plates and mitigate the adverse effects from the large out-of-plane deformation and potential local buckling failure, a novel laminated steel slit (LSS) shear wall assembled from two single-layer steel slit (SSS) shear walls is proposed in this study. First, the theoretical analysis method for predicting the shear strength and stiffness of the LSS shear walls is proposed. To validate the theoretical method as well as investigate the hysteretic performance of the LSS shear walls, two specimens made from different materials, common carbon steel and low yield steel, are designed and tested experimentally under quasi-static cyclic loading. Refined finite element models are developed to simulate the hysteretic behaviors of the LSS shear walls, which show good agreement with the test results. Further, the performance differences between the LSS shear walls and SSS shear walls are analyzed using the validated numerical simulation approach. The strength and stiffness of the LSS shear walls are greater than the summation of the individual SSS shear walls, attributed to the interaction between the different layers in the LSS shear walls. The energy dissipation efficiency of the LSS shear walls is improved and the stiffness degradation is effectively delayed, thanks to the incorporation of the low yield steel material. Finally, to evaluate the effects of the contributing factors on the seismic performance of the LSS shear walls, a series of parametric analyses are performed. Parametric analysis results show that the use of the low yield steel helps to improve the ductility and energy dissipation capacity of the LSS shear walls and delay the stiffness degradation. A large link width ratio, small link length ratio and large link thickness ratio can all contribute to a large strength, stiffness and absolute energy dissipation of the LSS shear walls, but the former two at the same time deteriorate the stiffness degradation.

Study on the cantilever ratio optimization of high-temperature molten salt pump for molten salt reactor based on structural integrity

The high-temperature molten salt pump is the core equipment in the small modular molten salt reactor with media temperatures up to 700 °C. The cantilever ratio of the molten salt pump is usually large. Excessively large cantilever ratios cause increased deformations and rotational amplitudes at the impeller, thus affecting the operational stability of the main pump; small cantilever ratios cause heavy temperature gradients, thus affecting the structural integrity evaluation. This paper used numerical simulation methods to calculate and analyze the temperature field, stress, and structural integrity, optimized the pump shaft cantilever length of the original scheme based on structural integrity using the dichotomy method, and analyzed the rotor dynamics of the optimization results. The results of this study show that the thermal expansion load caused by the temperature difference has a significant mechanical effect on the structure; the first-order critical speed of the rotor system of the optimized schemes has been improved, and the amplitude of the unbalanced response has been significantly reduced, which not only improves the operational stability of the rotor, also contributes to the compact design of the main pump of a small modular molten salt reactor.

Microstructure and Mechanical Property of the Large Cross-Sectioned Mg–Gd–Y–Zn–Zr Alloy Produced by Small Extrusion Ratio

Microstructure and Mechanical Property of the Large Cross-Sectioned Mg–Gd–Y–Zn–Zr Alloy Produced by Small Extrusion Ratio

A study of the response of reinforced concrete frames with and without masonry infill walls to earthquake motions

In developing countries prone to frequent earthquakes, it is common practice to use masonry infill walls as partitions in reinforced concrete frame buildings. Frames with infill have smaller drift demands and smaller drift capacities relative to similar frames without infill. Whether the relative reduction in drift demand offsets the plausible reduction in drift capacity remains open to discussion. This investigation provides experimental evidence on drift demands and drift capacities for both frames with and frames without infill. To make fair comparisons, only experiments where sets of nominally identical reinforced concrete frames, at least one frame with no infill and at least one frame with infill, are considered. Because many static experiments provide evidence for the reduction in drift capacity caused by infill, the objective of the dynamic experiments described in this study is to quantify the reduction in drift demand attributed to infill. Results of dynamic tests show that frames with infill drifted no more than one-third the amount similar frames without infill drifted in simulated base motions of the same intensity. Results of static tests show that the smallest drift capacities of frames with infill were approximately one-half of the drift capacities of similar frames without infill. These two experimental observations indicate that infill reduces drift demand more than it reduces drift capacity suggesting an overall beneficial effect of the infill. Field data were used to test this idea. Based on surveys of low-rise school buildings, RC frames with more full-height infill walls tend to have less earthquake damage than frames with less infill. A convenient method to quantify the amount of infill walls in buildings is computing wall ratios defined as the ratio of cross-sectional area of masonry infill walls on ground floor to total floor area above ground floor. Projections of the field data suggest that infill wall ratios of at least 0.5% in both directions of a building reduce the likelihood of severe structural damage by 300% compared with smaller ratios. The use of infill presents an inexpensive yet effective retrofit technique, even if only for temporary use, for strengthening buildings vulnerable to earthquake damage.

Origin of the Disparity between the Stability of Transmutated Mix-Cation and Mix-Anion Compounds

Transmutation is an efficient approach for material design. For example, ternary compound CuGaSe2 in chalcopyrite structure is a promising material for novel optoelectronic and thermoelectric device applications. It can be considered as formed from the binary host compound ZnSe in zinc-blende structure by cation transmutation (i.e., replacing two Zn atoms by one Cu and one Ga). While cation-transmutated materials are common, anion-transmutated ternary materials are rare, for example, Zn2AsBr (i.e., replacing two Se atoms by one As and one Br) is not reported. The physical origin for this puzzling disparity is unclear. In this work, we employ first-principles calculations to address this issue, and find that the distinct differences in stability between cation-transmutated (mix-cation) and anion-transmutated (mix-anion) compounds originate from their different trends of ionic radii as functions of their ionic state, i.e., for cations, the radius decreases with the increasing ionic state, whereas for anions, the radius increases with the increasing absolute ionic state. Therefore, for mix-cation compounds, the strain energy and Coulomb energy can be simultaneously optimized to make these materials stable. In contrast, for mix-anion systems, minimization of Coulomb energy will increase the strain energy, thus the system becomes unstable or less stable. Thus, the trend of decreasing strain energy and Coulomb energy is consistent in mix-cation compounds, while it is opposite in mix-anion compounds. Furthermore, the study suggests that the stability strategy for mix-anion compounds can be controlled by the ratio of ionic radii r 3/r 1, with a smaller ratio indicating greater stability. Our work, thus, elucidates the intrinsic stability trend of transmutated materials and provides guidelines for the design of novel ternary materials for various device applications.

Transient Thermal Spreading Resistance from Isothermal Source in a Circular Flux Tube

An analytical expression is developed for transient thermal spreading resistance from an isothermal circular source in a cylindrical flux tube as a function of constriction ratio and time. The flux tube is semi-infinite. The spreading resistance expression is obtained from the temperature expression by solving the heat equation. For short times, the dimensionless transient spreading resistance is proportional to dimensionless time based on the square root of the source area. For long times, the dimensionless spreading resistance approaches the values of the corresponding steady-state expression in the literature. For small constriction ratios, dimensionless spreading resistance approaches the classic isothermal half-space limit. A numerical analysis is presented which shows excellent agreement with the analytical solution. Approximate correlations for dimensionless resistance are also presented for both the isothermal and the isoflux cases.

Unveiling thermal stresses in RETaO4 (RE = Nd, Sm, Eu, Gd, Tb, Dy, Ho and Er) by first-principles calculations and finite element simulations

Thermal stress (σ) plays a critical role in regulating the stability and durability of thermal barrier coatings (TBCs) during service. However, its measurements are limited due to technical challenges. Here, thermal stresses in RETaO4 (RE = Nd, Sm, Eu, Gd, Tb, Dy, Ho, and Er) TBCs have been evaluated by a cross-scale model, integrating first-principles calculations and finite element simulations (FEM). The isobaric heat capacity, thermal expansion coefficients, density, Young's modulus, and Poisson's ratio of RETaO4 as a function of temperature have been determined by the quasi-harmonic approach (QHA) and the quasi-static approach (QSA). Taking these properties as the input data of FEM, the σ of TBCs with RETaO4 as ceramic coatings is estimated. It indicates that the maximum tensile stress exists at the ceramic and thermal-grown oxide coating interface. Notably, TBCs_NdTaO4 exhibits the highest tensile stress, reaching up to 2093 MPa, while TBCs_GdTaO4 has the lowest value at 1880 MPa. Furthermore, the key factors affecting σ are estimated using interpretable machine learning based on the decision tree algorithm. The RETaO4 with small Poisson's ratio, strong electronegativity, small heat capacity, and thermal expansion coefficients is helpful to achieving low σ in TBCs. GdTaO4, YTaO4 and (Ho0.5Er0.5)TaO4 emerge as more favorable options as ceramic layer due to their lower σ in TBCs. This present cross-scale model provides a successful tool for predicting σ and the reverse design of TBCs materials based on low σ in TBCs.

Numerical study on entropy minimization in pipes with helical airfoil and CuO nanoparticle integration

Abstract In this study, minimizing entropy generation in a horizontal pipe is numerically investigated through two passive techniques: in the first mode, the helical wire inserts in the pipe were placed at three various ratios of pitch ratio. The second mode is adding cupric oxide nanoparticles at various volume concentrations. Experiments were conducted for Reynolds numbers ranging from 4,000 to 14,000 under a uniform heat flux scenario of 25,000 W/m2. The study utilized the ANSYS 14.5 software, employing the K-omega standard model, which involves three primary governing equations: continuity, momentum, and energy. According to the data, it was determined that the helical wire placed inside the pipe with a small pitch ratio decreased the entropy generation number. Cupric oxide nanoparticles also have a substantial impact on the entropy generation number. The higher volume concentration models had lower entropy generation numbers and Bejan numbers than the other models. Comparative analyses further emphasize the substantial advantages of using cupric oxide nanofluids and helical-wire inserts, with efficiency gains ranging from 5.08 to 11.7%.

A Green High-k Dielectric from Modified Carboxymethyl Cellulose-Based with Dextrin.

Many crucial components inside electronic devices are made from non-renewable, non-biodegradable, and potentially toxic materials, leading to environmental damage. Finding alternative green dielectric materials is mandatory to align with global sustainable goals. Carboxymethyl cellulose (CMC) is a bio-polymer derived from cellulose and has outstanding properties. Herein, citric acid, dextrin, and CMC based hydrogels are prepared, which are biocompatible and biodegradable and exhibit rubber-like mechanical properties, with Young modulus values of 0.89 MPa. Hence, thin film CMC-based hydrogel is explored as a suitable green high-k dielectric candidate for operation at low voltages, demonstrating a high dielectric constant of up to 78. These fabricated transistors reveal stable high capacitance (2090 nF cm-2) for ≈±3V operation. Using a polyelectrolyte-type approach and poly-(2-vinyl anthracene) (PVAn) surface modification, this study demonstrates a thin dielectric layer (d ≈30 nm) with a small voltage threshold (Vth ≈-0.8 V), moderate transconductance (gm ≈65 nS), and high ON-OFF ratio (≈105). Furthermore, the dielectric layer exhibits stable performance under bias stress of ± 3.5 V and 100 cycles of switching tests. The modified CMC-based hydrogel demonstrates desirable performance as a green dielectric for low-voltage operation, further highlighting its biocompatibility.

Numerical simulation of the effect of jet small orifice structure on cavitation characteristic and jet impact flow field

The jet impingement-negative pressure deamination reactor (JI-NPDR) is a continuous, non-clogging, and efficient deamination equipment characterized by its simple structure. Research has demonstrated that the fluid passing through the jet orifices in the jet impact section of the reactor leads to partial cavitation. This situation directly impacts the flow characteristics before jet impact and the gas-liquid separation behavior in the negative pressure separation section. Therefore, this work proposes to utilize the CFD numerical simulation method to analyze the fluid cavitation evolution rules under the aspect ratio l/d structure of different jet orifices and to investigate the influence of orifice structure on the jet impact flow field. The results indicate that an increase in the liquid flow rate and the small orifice aspect ratio l/d promotes the conversion of pressure energy to kinetic energy, leading to an increase in cavitation intensity in the jet orifice. Furthermore, the evolution behavior of the jet impact flow field can be effectively controlled based on the l/d structural parameter of the small orifice aspect ratio. The research results can provide fundamental data support for the structural optimization design and engineering application of the JI-NPDR.

Theoretical and experimental study of the spanwise effect of turbulence on the aerodynamic lift on a wing with different aspect ratios

In this paper, a combined theoretical and experimental study is carried out to investigate the spanwise effect of turbulence on the aerodynamic lift on a wing with different aspect ratios. The ratio of the mean square variance of the aerodynamic lift calculated by the commonly used strip theory and the two-wavenumber buffeting theory is analyzed comprehensively for the wings with different aspect ratios in turbulence with various integral scales. To validate the theoretical analysis and achieve a deeper understanding of the spanwise effects of turbulence, wind tunnel experiments are performed on National Advisory Committee for Aeronautics 0015 airfoils in grid-generated turbulent flows with different integral scales. The results demonstrate that it is essential to use the two-wavenumber buffeting theory to account for the spanwise effect of turbulence when calculating the aerodynamic lifts on wings with small aspect ratios, especially when in small-scale turbulence. The deviations between the equivalent two-wavenumber coherence function and the spanwise effect influence function at low reduced streamwise wavenumbers are the underlying causes for spanwise effects of turbulence. To achieve reliable wind tunnel testing results, appropriate simulations of the ratio of the turbulence integral scale to the chord are very important in the measurements of aerodynamic lifts on finite-span wing sections, especially for those with small aspect ratios.