Semi-empirical Formula Research Articles

Fractal dimension analysis of concrete specimens under different strain rates

To analyze the relationship between the dynamic mechanical performance and fractality of concrete, the specimens of a separate Hopkinson pressure bar (SHPB) from a concrete component using the coring method were obtained. This study designed three common concrete strength grades, C40, C50, and C60 and conducted dynamic splitting tensile tests, together with scanning electron microscopy (SEM) tests on these specimens. Based on the experimental results, the variations in the dynamic splitting strength (DSTS), dynamic increase factor (DIF), and energy absorption (EA) efficiency were analyzed. A semi-empirical formula for a unified DIF value was proposed. A digital image algorithm based on fractal theory was designed to evaluate the fractal dimension (FD) of the impact damage area crack pattern, and regression models were established between strain rate, DIF, and FD. Based on SEM tests, the relationship between dynamic splitting of the core sample and microstructure was analyzed, and a model was established between FD of SEM image and strain rate. The test results demonstrated that the dynamic mechanical performance of concrete has a significant strain-rate effect. The damage characteristics of concrete under impact can be quantitatively evaluated by the FD characteristics under impact loads, and there was a significant correlation between the strain rate, DIF, and crack FD. The internal and interaggregate cracking of the core samples increased and expanded continuously. The change in microstructure was consistent with the changes in the macroscopic failure modes, and FD of the specimen pore area increased with an increase in the strain rate. The research results organically linked FD and dynamic performance, failure mode, SEM images, and other mechanical attributes, providing a reference for using image information to study the dynamic mechanical performance of concrete materials.

Heat Transfer Analysis and Structural Optimization for Spiral Channel Regenerative Cooling Thrust Chamber

There is currently a lack of efficient heat transfer analysis methodologies for spiral channel regenerative cooling that has been increasingly applied in liquid rocket engines. To figure out the heat transfer characteristics of the spiral channel regenerative cooling thrust chamber, a simple 1D method based on the traditional semi-empirical formula after correcting the flow velocity is proposed. The accuracy of this approach is verified by the 3D numerical simulation. The verified method is further used to analyze the distribution of inner wall temperature in the test case and optimize the channel’s parameters. The research shows that the maximum inner wall temperature cooled by the spiral channel is 8.5% lower than that of the straight channel under the same channel size and boundary condition, indicating that the application of the spiral channel significantly improves the cooling effect. In addition, the 1D model combined with the second-order response surface model is employed to optimize the channel width, channel height, pitch, and inner wall thickness aiming for the best cooling effect. The calculated maximum temperature of the inner wall after the structure optimization is 586.6 K, which is 29.8% lower than the initial structure before optimization.

Improving the Overall Efficiency of Marine Power Systems through Co-Optimization of Top-Bottom Combined Cycle by Means of Exhaust-Gas Bypass: A Semi Empirical Function Analysis Method

The mandatory implementation of the standards laid out in the Energy Efficiency Existing Ship Index (EEXI) and the Carbon Intensity Indicator (CII) requires ships to improve their efficiency and thereby reduce their carbon emissions. To date, the steam Rankine cycle (RC) has been widely used to recover wasted heat from marine main engines to improve the energy-conversion efficiency of ships. However, current marine low-speed diesel engines are usually highly efficient, leading to the low exhaust gas temperature. Additionally, the temperature of waste heat from exhaust gas is too low to be recovered economically by RC. Consequently, a solution has been proposed to improve the overall efficiency by means of waste heat recovery. The exhaust gas is bypassed before the turbocharger, which can decrease the air excess ratio of main engine to increase the exhaust gas temperature, and to achieve high overall efficiency of combined cycle. For quantitative assessments, a semi-empirical formula related to the bypass ratio, the excess air ratio, and the turbocharging efficiency was developed. Furthermore, the semi-empirical formula was verified by testing and engine model. The results showed that the semi-empirical formula accurately represented the relationships of these parameters. Assessment results showed that at the turbocharging efficiency of 68.8%, the exhaust temperature could increase by at least 75 °C, with a bypass ratio of 15%. Moreover, at the optimal bypass ratio of 11.1%, the maximum overall efficiency rose to 54.84% from 50.34%. Finally, EEXI (CII) decreased from 6.1 (4.56) to 5.64 (4.12), with the NOx emissions up to Tier II standard.

The solitary wave run-up on sloped beaches protected by submerged rigid breakwaters

The reduction of wave run-up induced by solitary waves at sloping beaches, by means of submerged barriers has been investigated. To this purpose, 198 laboratory tests were undertaken in the wave channel of the University of Calabria, by adopting three beach slopes, three water depths and square and rectangular rigid type-barriers. To make comparisons on the performance of the barriers in reducing the run-up, 99 tests were carried out considering the same experimental conditions, without the barriers. Two approaches were used to deduce the resulting solitary wave run-up in the presence of the barriers starting from the knowledge of wave parameters without them. The first approach uses the wave amplitude, whereas the second, more physically based, uses the wave energy, depending on the horizontal velocity and the wave pressure. Based on the calculation of the transmission coefficients using the dimensional analysis, the transmitted wave amplitude and energy after the barriers were deduced. Using these quantities, the recent semi-empirical formulas deduced by Casella et al. (2022) in the absence of the barriers were extended to determine the solitary wave run-up in their presence.

The impact of group velocity dispersion on femtosecond laser filamentation with higher-order Kerr effect at different atmospheric pressures

The impact of group velocity dispersion (GVD) on femtosecond laser filamentation with the higher-order Kerr effect is studied at different atmospheric pressures. The results show that GVD makes the collapse distance to not meet the semi-empirical formula proposed by Dawes and Marburger, suppresses multiple focusing and splitting in time during the propagation process, and reduces the length of filament. In addition, we also compared the results with those considering only the third-order Kerr effect. This provides some information for the study of whether the defocus effect in the femtosecond laser filamentation is the higher-order Kerr effect or the plasma effect.

Theoretical studies on structural properties and decay modes of $$^{284-375}$$119 isotopes

Within the axially deformed relativistic mean field with $$\hbox {NL3}^*$$ parametrisation, the different bulk properties like binding energy, quadrupole deformation parameter, separation energies, density profile and shape co-existence for Z = 119 isotopic chain within the mass range 284 $$\le$$ A $$\le$$ 375 are computed. Further, a competition between possible decay modes such as α-decay, $$\beta$$ -decay and spontaneous fission (SF) of the isotopic chain of Z = 119 superheavy nuclei under study is systematically analysed within self-consistent relativistic mean field model and a close agreement is noticed among the calculations performed using various semi-empirical formulae and also with the estimations made by finite range droplet model (FRDM) wherever available. Our analysis confirmed that α–decay is restricted within the mass range 284 $$\le$$ A $$\le$$ 375 and thus being the dominant decay channel in this mass range and there is no possibility of $$\beta$$ –decay for the considered isotopic chain. In addition, we forecasted the α–decay chain of fission survival nuclides, i.e. $$^{284-296}119$$ and found as one α chain from $$^{284} 119$$ and $$^{296} 119$$ , $$2 \alpha$$ chains from $$^{285}119$$ and $$^{295} 119$$ consistently, $$3\alpha$$ chains from $$^{286} 119$$ and $$^{294} 119$$ consistently, $$4 \alpha$$ chains from $$^{287} 119$$ consistently, six consistent α chains from $$^{288-293} 119$$ . A comparative study of SF and α-decay half-live computed using the formula of Santhosh et al and Coulomb proximity potential model (CPPM), respectively, for the fission surviving isotopic chain reveals that isotopes $$^{288-293} 119$$ exhibit $$6\alpha$$ chains followed by SF, isotopes $$^{295,296} 119$$ exhibit $$4\alpha$$ chains followed by SF, and the rest of the nuclei show continuous α chains. This study has also established that the alpha half-life values computed using $$\hbox {Q}_\alpha$$ (RMF) agree with half-life values computed using experimental $$\hbox {Q}_\alpha$$ values within 1 order difference. Thus, such studies can be of great significance to the experimentalists in very near future for synthesizing the isotopes of Z = 119 superheavy nuclei.

Meta-analysis of a large bedload transport rate dataset

The estimation of bedload transport, a type of coarse fluvial sediment motion, is challenging because of higher-order, complex, and time-variable environmental processes. Still, models for calculating bedload transport mostly rely on semi-empirical formulae derived from time-averaged laboratory flume or field measurements and involve cross-section averaging of hydro-environmental parameters. Additionally, many models assume infinite, constant availability of sediment, which is unrealistic in natural environments. While most published models yield excellent results on the dataset they were trained on, they may be significantly inaccurate when applied to other cases. Also, more recent formulae relying on considerable amounts of data still lead to high calculation uncertainty. While the importance of short-term dynamics, for example, driven by turbulence, for bedload transport is well known, this study investigates the relevance of time-variable processes at monthly to seasonal scales. Our analysis of a large dataset and remote sensing data shows evidence for seasonal variability in measurements of bedload transport rates and challenges the validity of Gaussian statistics for interpolating bedload transport models. Measured bedload transport rates were smaller when snowmelt was taking place and when no glacier was present in the catchment, and were best represented by extreme value distributions. By controlling for biases from measurement devices, geomorphic patterns, and the presence of an upstream dam, we show that steady, constant at-a-station hydraulics only explain a limited share of the variance in the measurements. Ultimately, a model for estimating bedload transport rates should consider the temporal variability of processes across all scales, from turbulence to climate.

Evolution of the Phase and Hydrogen Storage Properties of New-Type VTiCrFeMn High-Entropy Alloy Prepared via Mechanical Alloying

High-entropy alloys (HEAs) have ample space for composition design, so finding an ideal hydrogen storage material is a great challenge. This work used the atomic radius difference, valence electron concentration, entropy, enthalpy, and new design parameters to develop a new-type alloy with a BCC structure. The V35Ti25Cr20Fe10Mn10 alloy was selected by semi-empirical formula calculation, subsequently, the alloy was successfully synthesized by mechanical alloying, and hydrogen storage properties were evaluated. The activated sample shows an excellent kinetic performance of hydrogen absorption, but its maximum hydrogen storage capacity is only about 0.34 wt.%. The results of the PCI test show that the hydrogen absorption way may be composed of the H-solid solution in the alloy and the formation of a few hydrides, which determines the hydrogen storage capacity. Significantly, the design method reported in this paper can meet the composition design of most HEAs, which has a broad application prospect.

A systematic analysis for one proton radioactivity of ground state nuclei

We systematically studied proton radioactivity half-lives in the atomic number range 53≤Z≤83 using macroscopic models such as Coulomb and Proximity potential model, effective liquid drop model (ELDM), Generalized liquid drop model (GLDM), Universal decay law for proton emission (UDLP), Gammow-like model (GLM) and Unified fission model (UFM). The proton decay half-lives produced by the macroscopic models are compared with those of semi-microscopic approach such as DDM3Y and using effective interaction potentials such as JLM, M3Y+EX, R3Y+EX, SLy4, SRG, SKC and SKD. After detail analysis, it is found that among macroscopic models ELDM and semi-empirical formula UDLP produce proton decay half-lives close to experiments. Furthermore, among semi-microscopic approach, DDM3Y produces proton decay half-lives close to the experiments. Thus, Both ELDM and DDM3Y model can be effectively used in the prediction of half-lives of unexplored proton emitters.

Critical properties and phase behavior of confined fluids in irregular nanopores of shale gas reservoir

Real pore size and shape can induce critical properties shifts and phase behavior alterations for confined fluids in nanopores and impact the gas storage and transport mechanisms in shale gas reservoirs. Therefore, accurate calculations of phase behavior parameters in irregular nanopores are of great significance for the efficient development of shale gas reservoirs. No publications so far have been found to study the critical properties shift of confined fluids in irregular nanopores. In this paper, first, a quantitative description method for calculating the adsorbed volume of a multicomponent confined fluid in irregular nanopores is proposed, coupled with scanning electron microscope (SEM) images of shale cores and a semi-empirical formula for adsorbed thickness. Second, an effective molar volume correction method is extended to non-circular pores. Meanwhile, a new parameter is introduced to modify a molar volume term. Third, a novel correlation is proposed to predict the critical properties shifts in irregular nanopores considering pore shape and mixed fluid composition. Finally, a modified PR-EOS (Peng-Robinson equation of state) model is proposed, solved, and validated. Moreover, the critical parameters of pure component fluids and phase behavior characteristics of mixed hydrocarbons under different pore sizes, pore shapes, and hydrocarbon components are investigated, which reveals that a real pore structure and mixed fluid composition in shale gas reservoirs can change phase behaviors of confined fluids in nanoscale pores.

Analytical method for predicting tunnel heave due to overlying excavation considering spatial effect

Deep excavations have significant influence on existing metro tunnels. Currently, there is still a lack of practical and simple assessment approaches for predicting this influence. In this paper, a new analytical method is developed that uses a continuous Euler-Bernoulli beam to simulate shield tunnel behavior due to overlying basement excavation. Firstly, the excavation-induced greenfield displacement at the tunnel axis is obtained with the application of Mindlin’s solution. Secondly, the longitudinal response of the tunnel due to the ground movement induced by excavation is computed using a finite difference method. The effectiveness and applicability of the proposed method are validated by three high-quality case histories, including field measurement, FEM method, and semi-analytical method. Different from previous studies, the tunnel-soil interaction behavior is studied based on the displacement coupling condition in the proposed method, capable of accurately considering tunnel-soil interaction behavior. Subsequently, with the verified proposed analytical solution, further parametric studies are performed to investigate the spatial factors affecting tunnel behavior including tunnel buried depth, excavation-tunnel relative distance, excavation geometry, skew angle between tunnel axis, short side of the excavation, and excavation depth, yielding abundant artificial data. Then, a semi-empirical formula considering spatial effect is established for directly predicting the maximum vertical displacement of the tunnel with adequate engineering accuracy and applicability. The proposed analytical method can be applied to predict the potential risk of existing tunnel due to nearby excavation.

A study of proton-induced reactions on natural Silicon targets

Experimental excitation functions of isotopes produced in reactions p + natSi are compared with the results of nuclear reaction program TALYS 1.95 and semi-empirical cross section formulas. We consider excitation functions of 7 isotopes (28Mg, 26Al, 24,22Na, 18F and 10,7Be) produced in reactions at bombarding energies of 20-144 MeV. They are compared with the predictions of the code TALYS 1.95, the semi-empirical formulas of Silberberg-Tsao (code yieldx) and SPACS. Comparisons of the results of the code TALYS 1.95 and previously published results of code ALICE are made. The predictive power of code TALYS 1.95 may be questioned for reaction products with mass number very much smaller than the target and of semi-empirical formulas at lower energies.

A study of the reaction 55Mn(p,4n)52Fe: excitation function and medical applications

The present study concerns the medical applications and production of 52Fe via the reaction 55Mn(p,4n)52Fe together with the reference reaction 27Al(p,x)22Na employed in cross section measurements. Experimental excitation functions from threshold up to 200 MeV are compared with the predictions of the TALYS 1.95 code and the semi-empirical formulas SPACS and Silberberg & Tsao. We obtained two TALYS parameter sets for the 55Mn(p,4n)52Fe and 27Al(p,x)22Na reactions which give a good description of the excitation functions for energies up to 85 MeV. Discrepancies observed at higher energies require further investigation. The semi-empirical formulas provide a good description of the excitation functions above 120 MeV.

Discussion on Static Resistance of Granite under Penetration.

A total of 9 tests were carried out with 30 mm and 78 mm caliber scaled projectiles penetrating into granite targets. The penetration depth, crater diameter, and mass loss rate were examined and discussed. The results indicate that the dimensionless penetration depth of large-caliber projectiles is 20% greater than small-caliber projectiles. Based on the description of static resistance Ra in the Forrestal semi-empirical formula, the size effect of dimensionless penetration depth can be attributed to the size effect of static resistance Ra, and it can be seen that the penetration static resistance of projectile A is 40% higher than that of projectile B. Numerical simulations of projectile penetration into granite targets were conducted using the finite element program ANSYS/LS-DYNA. In terms of penetration depth and crater damage, the numerical simulation results agree well with the test data. This suggests that the selection of parameters was reasonable. The influence of compressive strength, projectile striking velocity, mass, diameter, and caliber-radius-head (CRH) ratio on the static resistance Ra were studied by RHT model parameterization. Based on the numerical results from the parametric study, an empirical formula was derived to predict the static resistance Ra.

Theoretical Investigation of Electron–Ion Recombination Process of Mg-like Gold

The L-shell dielectronic and trielectronic recombinations of highly charged Mg-like gold ions (Au67+) in the ground state 2s22p63s2 1S0 have been studied systematically. The recombination cross-sections and rate coefficients are carefully calculated for ∆n = 1 (2s/2p → 3l) transitions using a flexible atomic code based on the relativistic configuration interaction method and considering the Breit and QED corrections. Detailed resonance energies and resonance strengths are presented for the stronger resonances of the LMn (n = 3–12) series. It is found that the contributions of the trielectronic recombination to the total cross-section is about 13.75%, which cannot be neglected. For convenience of application, the plasma rate coefficients are also calculated and fitted to a semiempirical formula, and in the calculations, the contributions from the higher excited resonance groups n ≥ 13 are evaluated by an extrapolation method, which is about 2.93% of the total rate coefficient.

Development and verification of helium–xenon mixture cooled small reaction system

Although Helium–Xenon mixture cooled small reactor has been widely concerned, there is no mature thermal calculation software that can be applied to Helium–Xenon mixture cooled small reactor in China. In this paper, a semi empirical formula used to predict the physical properties of binary inert gas mixtures is used to establish a physical property calculation model of Helium–Xenon mixture gas mixtures, and the flow and heat transfer calculation model, turbine model and compressor model are modified and improved, so as to achieve the calculation of the Brayton cycle system. The function of the original system analysis program is expanded and improved, and the simulation program for he xenon mixed gas reactor system is developed. At the same time, the closed Brayton cycle system is established by using the system analysis program developed in this paper, and the calculation results are compared with the design values. The maximum relative error is 6.9%. The steady-state operation results of the model are in good agreement with the design operation parameters, which proves the applicability of the improved simulation model. The steady-state response characteristics analysis, the introduction of positive and negative reactivity accidents and the calculation of transient conditions such as step load drop of the reactor were carried out. The overall trend is the same as the literature survey results. The results show that the system analysis program developed in this paper is suitable for the analysis of the Brayton cycle system of Helium–Xenon mixture cooled small reactor.

New Geiger-Nuttall law for cluster radioactivity half-lives* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the construct program of the key discipline in hunan province, the Research Foundation of Education Bureau of Hunan Province, China (18A237), the Shandong Province Natural Science Foundation, China (ZR2022JQ04), the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle

In this study, derived from Balasubramaniam's formula [Phys. Rev. C 70, 017301 (2004)] and further considering the effect of the parent nucleus mass, blocking effect, and effect of reduced mass on cluster radioactivity half-lives, we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the half-lives of this process for 16 even-even nuclei and 10 odd-A nuclei. For comparison, a single universal curve for cluster radioactivity and α decay proposed by Poenaru [Phys. Rev. C 83, 014601 (2011)], a scaling law proposed by Horoi [J. Phys. G: Nucl. Part. Phys. 30, 945 (2004)], an extension of the Viola-Seaborg formula from α decay to cluster radioactivity proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)], a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives, with the least rms being 0.606, and are better than the compared values. Moreover, we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

New semi-empirical systematic of (p,n) reaction cross section at 7.5 MeV

Abstract It is advised to use a new formula to calculate the (p, n) reaction cross section at 7.5 MeV. We propose six new parameters for the formula proposed by Broeders, C. and Konobeyev, A.Y. (2008. Systematics of (p,n) reaction crosssection. Radiochim. Acta 96: 387–397) to fit experimental data. It should be noted that our systematics is only applicable to isotopes with a ratio of 7.5 MeV to the reaction threshold above 1.3 (7.5/E th > 1.3). This is based on analytical calculations generated from the semi-empirical mass formula, the evaporation model, and the pre-equilibrium exciton model. We were able to find new parameters for the Broders et al. formula through this inquiry that guarantee a good fit with the revised experimental data (EXFOR2022) and provide a minimum value for the statistical parameters ∑ and χ 2.

Formation of droplets of yield stress non-Newtonian fluids at T-junctions within parallelized microchannels

The effects of yield stress on the flow pattern, and the breakup mechanism, formation frequency and size of droplets at T-junctions within symmetrical parallelized microchannels are investigated experimentally. Carbopol gel and cyclohexane with 5 wt% span 20 are used as dispersed and continuous phases, respectively. Three flow patterns are observed, including parallel flow, jetting flow-elongated droplets, and dripping flow-slug/cloud droplets. Based on the yield stress characteristics, the breakup dynamics of the liquid–liquid interface during droplet formation under different flow patterns, flow rates and Carbopol concentrations are studied. The results reveal that the yield stress would enlarge the thickness of liquid film, weaken the squeezing force of the continuous phase and enhance the resistance of the dispersed phase, which greatly slow down the droplet formation. Finally, the stable and uniform operating ranges of liquid–liquid two-phase flow in yield stress non-Newtonian fluids are obtained, and the semi-empirical formulas for droplet size prediction are established.

Experimental study on flame merging of two parallel rectangular fire sources with ground effect

This paper investigates the flame merging process of two parallel rectangular fire sources with ground effect. The experiments were carried out with different burner sizes (aspect ratio w/d = 1–3), heat release rates per unit area Q″ and burner spacings s. It is found that the flame interaction is weak when w/d = 1 and the flame merging process could be further divided into four states. The relationship between the flame merging probability P and the dimensionless burner spacing s/Zf0 (Zf0 is the flame height of one single fire) could be described by the Boltzmann function. The coefficient a and b of the function have definite physical significance and increase with w/d. An exponential function correlates a, b and w/d, and a semi-empirical model of P is established. A correction factor C constructed with P and As=0/d (As=0: short side length of the overall fire source when s = 0) is proposed to correct the dimensionless heat release rate Q˙d*. Thus, the characteristic dimension d of one single fire could be applied to the whole flame merging process. A semi-empirical formula is developed to describe the relationship between the dimensionless flame height L/d and CQ˙d*.