Empirical Formula For Calculation Research Articles

A new empirical formula for calculation of (n,3n) cross sections of heavy mass nuclei in the energy region 22–27.5 MeV

In this paper we want to study (n,3n) reactions using an empirical formula derived on the basis of the statistical model considering reaction Q-value dependence. This formula was obtained by taking into account the exponential dependence on asymmetry parameter (N−Z)/A for neutron-induced reactions in Levkovskii's empirical formula. In addition, the present formula depends also on incident energy En, reaction Q-value and symmetry term (N−Z)2/A. Herein, a new analysis of experimental data of (n,3n) reactions in the energy region 22–27.5 MeV was carried out for quick estimation of cross sections of the heavy mass isotopes of odd Z-even N nuclides in the region of A = 151 to 209. We observed a good agreement of the experimental cross section data with the calculations performed using the present empirical formula.

Research on the Deformation Law and Stress Distribution Characteristics of Overburden under the Influence of Multiple Faults

Taking the geological conditions of a coal mine in Liupanshui City, Guizhou Province, as the background. The fracture law of the roof in the coal face and the height of the “Two zones” were obtained through theoretical analysis and empirical formula calculation, and the results were verified using similar simulation experiments. Through numerical simulation were researched the stress distribution characteristics of the overlying strata on the working face under the influence of multiple faults. The results showed that in the early stage of mining, F1 undergoes activation under the influence of the main roof weighting, leading to an increase in the degree of plastic damage to the coal seam and strata behind the working face, causing a redistribution of the behind abutment pressure. Finally, under the influence of the F1 barrier effect, the vast majority of the behind abutment pressure is transferred to the lower strata of F1, leading to a continuous increase in stress concentration there. But as the working face continues to advance, the blocking effect of the roof plastic zone above the goaf on the transmission of the behind abutment pressure of the working face begins to appear and continues to increase, leading to a decrease in the peak stress at the lower strata of F1. The stress change process on the F2 side is similar to that on the F1 side, the front abutment pressure is initially distributed in the strata in front of the working face, but as the activation degree of F2 continues to intensify, it gradually shifts to the lower strata of F2, and ultimately the majority of the front abutment pressure is borne by the lower strata of F2.

Landslide risk evaluation method of open-pit mine based on numerical simulation of large deformation of landslide

It is of great practical significance to carry out quantitative risk assessment of landslide disaster to protect people’s lives and property safety and maintain the sustainable development of social economy. The delineation of landslide disaster range is the key link of landslide risk evaluation in open-pit mine. This study took the open-pit coal mine coal mine in Block I of Thar coal field in Pakistan as the research background, and constructed a framework for landslide risk evaluation in open-pit mines. Based on the numerical simulation method of large deformation of landslide, the disaster range of landslide in open-pit mine was delineated. The stability of stope slope was analyzed based on rigid body limit equilibrium method. The probability of landslide instability was calculated based on Monte Carlo method. And the comprehensive fuzzy evaluation model was established to calculate the total risk value of landslide. The results showed that: through numerical simulation and empirical formula calculation, the landslide disaster range was accurately delineated, and the comprehensive vulnerability of the disaster bearing body was determined to be medium vulnerability; the annual probability of landslide instability under natural conditions was 0.003, which belongs to moderate risk. The annual probability of landslide instability under rainstorm conditions was 0.024, which was highly dangerous; the annual probability of landslide instability under seismic conditions was 0.018, which was highly dangerous. Under natural conditions, the total risk value of landslide was 114,686.4 rmb, and the annual mortality rate of population was 0.0255 people/year. The total risk value of landslide under rainstorm condition was 11,707,570 rmb, and the annual mortality rate of population was 0.18375 people/year. The total risk value of landslide under earthquake condition was 43,007,400 rmb, and the annual mortality rate of population was 0.135 person/year, which was an unacceptable risk. The economic loss was a small geological disaster risk under natural conditions, and it was a medium-sized geological disaster risk under both rainstorm and earthquake conditions. Therefore, landslide prevention and control and management measures such as slope deformation monitoring were proposed to ensure the safety of personnel and property in open-pit mines.

Dynamic stiffness of polyester fiber mooring ropes: Experimental investigation based on radial basis function neural networks

Traditional steel wires are being replaced with mooring ropes made from synthetic fibers in offshore industries. However, under the long-term influence of a wave load, the dynamic response of a rope is extremely complex. This paper presents a comprehensive experimental study of the nonlinear dynamic stiffness of polyester fiber mooring ropes under cyclic loading. The stress–strain characteristics of the fiber ropes were investigated based on experimental data. Moreover, cyclic load tests with different mean loads, load amplitudes, and cycles were conducted to study the effects of these three parameters on dynamic stiffness. In previous studies, the dynamic stiffness of fiber ropes was estimated using empirical equations. In this study, the self-learning ability of a radial basis function (RBF) neural network was used to predict the dynamic stiffness of polyester fiber ropes. The predicted results were compared with the empirical formula calculations and experimental measurement results. The RBF neural network has better prediction results than the empirical formulation. In addition, the autonomic learning of the neural network was better when the sample data were in a disordered input state than in an ordered input state. The research findings of this study provide new approaches for solving the dynamic stiffness of ropes and lay a theoretical foundation for the mechanical analysis in the engineering design stage of mooring systems.

Experimental investigation of steel fiber reinforced concrete slabs subjected to underwater contact explosions

Fiber reinforced concrete has gained significant attention due to its higher ductility and flexural behavior, making it a promising material for resisting extreme loads such as those caused by blast and impact. In this study, we present experimental results from static tests conducted on steel fiber reinforced concrete with different content of hooked end steel fibers and concrete strength. Underwater contact explosion tests were performed for 6 pieces of 50 cm × 50 cm x 6 cm steel fiber reinforced concrete slabs. The damage patterns observed in the slabs were analyzed, and shock pressure data was measured and compared with empirical formula calculations. Test results demonstrate that the addition of steel fiber effectively enhances the compressive and tensile strength of concrete while also significantly improving its anti-explosion capacity. In contrast, the plain concrete slab (control group) displayed an overall state of failure during underwater contact explosions. Steel fiber reinforced concrete slabs primarily experienced bending failure and “Y" crack damage, accompanied by local collapse failure on the back surface. Overall, these findings suggest that steel fiber reinforced concrete holds great promise as a superior material for resisting extreme loads, particularly in marine environments.

Damage characteristics of cabin in navigational state subjected to near-field underwater explosion

An arbitrary Lagrange-Euler (ALE) method is used to establish a numerical model for the fluid-structure interaction of near-field underwater explosion while cabins are under sailing conditions. First, the ALE method is used to calculate shock wave and bubble pulsation loads of free field underwater explosion. The results show that the values of shock wave peak, bubble fluctuation period, maximum radius of bubble are similar to empirical formula calculation, which verifies the accuracy of ALE method in calculating explosion loads. On this basis, from the aspects of local damage, longitudinal strength and impact environment of cabin structure, the dynamic response characteristics of cabin structure under the coupling of impact and bubble load at a certain speed and different explosion distance are analyzed and compared with that at static condition. The results show that compared with the static state, the local damage is weakened, the longitudinal strength is increased, the difference of longitudinal strength between navigation and static state is 7%–12%, the shock spectrum value of the compartment corresponding to the explosion source is reduced, and the shock spectrum value of the adjacent compartment is slightly increased; When the cabin is sailing, the increase of the explosion distance within the maximum radius of bubble pulsation increases the action area of bubble pulsation load, and the effect of bubble pulsation load is enhanced, but the coupling enhancement of explosion load is difficult to appear, so that the damage of cabin structure is reduced. The working condition of the cabin suffering from near-field underwater explosion damage under the navigational state analyzed in this paper is closer to the reality, and more truly reflects the process of underwater explosion shock wave and bubble load coupling applied to cabins, which lays a foundation for the fuze warhead coordination design and relevant parameter setting when the torpedo and other underwater weapons give full play to the damage efficiency.

DOSE CALCULATION OF PROTON THERAPY BASED ON MONTE CARLO AND EMPIRICAL FORMULA.

In this work, we used the Monte Carlo-based TOPAS simulation software to calculate the ambient dose equivalents and annual effective dose due to the secondary neutron field produced in proton therapy, also we introduced a USTC phantom to access the organ equivalent dose. The ambient dose equivalent and annual effective dose were calculated in several positions of interest inside and outside the facility. The simulation results were compared qualitatively to the results of the Empirical Formula, showing that the Empirical Formula calculations overestimated the dose, 28.95 times higher than the MC simulations, on average, which would lead to over shielding. In addition, the highest equivalent dose rate of a single radiation-sensitive organ simulated by TOPAS was 1.50×10-9mSv/a for the eye lens, 2.36×10-3mSv/a for limbs and 1.01×10-3mSv/a for skin, which also meets the limits. Therefore, MC simulation has great advantages in shielding design and safety evaluation. And this work presents a new method to calculate the dose, introducing a more anthropogenic phantom can get more realistic results.

Determination of the Height of Overburden Water-Conducting Fracture Zone in 215102 Working Face of Yue Nan Coal Mine

In order to extract gas accurately in Yue Nan coal mine and prevent gas over limit and gas accidents, a combination of theoretical analysis and numerical simulation was used to investigate the height of the overburden caving zone and fracture zone in the working face, using 215102 working face as the engineering background. The results show three key strata in the 215102 working face, namely siltstone, sandy mudstone, and sandy mudstone. The empirical formula’s calculation results are in good accord with the findings of the theoretical analysis, which indicates that the height of the water-conducting fracture zone created by mining in 215102’s working face is 87.35 m. The plastic zone, stress distribution and displacement variation of the model overburden of the working face were analyzed separately in the numerical simulation. The results of the plastic zone simulation show that the caving zone’s maximum height is about 15.96 m, and the fracture zone’s maximum height is approximately 82.39 m. The stress distribution shows that the caving zone’s greatest height is around 13.65 m, while the fracture zone’s maximum height is roughly 77.24 m. The amount of overburden subsidence proves that the caving zone’s maximum height of about 10.08 m, and the fracture zone’s maximum height of approximately 82.69 m. The height of the overburden caving zone and fracture zone of 215102 working face are ultimately found to be 14.02 m and 76.42 m, respectively, based on theoretical analysis, empirical formula calculation, and numerical simulation findings.

Structural Design of Ocean Temperature and Depth Sensor with Quick Response and High Sensitivity

The electrical sensing elements used in the traditional XBT (Expendable Bathythermograph) have problems such as low sensitivity and slow response time, and it is difficult to overcome the complex marine environment using the time–depth formula. In this paper, an ocean temperature depth sensor based on brass diaphragm and liquid filling is designed. The stress response time of FBGs with different lengths and the heat transfer time of different liquid materials are compared, and it is found that a fast response of 51 ms can be obtained by using GaInSn liquid for temperature sensing. The center deflection changes of brass diaphragms with different radii are analyzed, and the brass diaphragms with radius and thickness of 10 mm and 1 mm are selected, which still have good elastic properties under the pressure of 5 MPa. The influence of the inner metal shell section radius on the temperature and depth sensitivity is analyzed. When the final section radius is 3 mm, the temperature sensitivity of the sensor is 1.065 nm/°C, the pressure sensitivity is 1.245 nm/MPa, and the response time of temperature and depth is relatively close. Compared with the traditional temperature and depth sensors using empirical formulas for calculation, the data accuracy is improved, and a wide range of sensitivity can be tuned by adjusting the size of the internal metal shell, which can meet the needs of ocean temperature and depth data detection with high sensitivity and fast response time.

Study on explosion resistance process simulation and blast fracture failure of Ti[sbnd]6Al[sbnd]4V titanium alloy sheet

The application of high-strength and high-toughness titanium alloy in armour protection is increasing with its excellent properties. However, there is little research on titanium alloy in explosion protection, especially the dynamic response process under localised explosion load and finite element simulation of the explosion resistance process of titanium alloy sheet. In this paper, the deformation and fracture failure features of the 1.6 mm thick Ti6Al4V titanium alloy sheet during the blast loading process were studied by combining LS-DYNA finite element simulation and air explosion experiments. The error of the overpressure peak value of explosion shock wave between the value obtained by improved theoretical empirical formula calculation of cylindrical charge and the value obtained by numerical simulation is only 0.2%. By studying the influence of explosive shape and air domain mesh size on the overpressure value in the process of detonation wave propagation, the Structured Arbitrary Lagrangian-Eulerian (S-ALE) algorithm was selected for finite element simulation. When the air domain mesh size is 1 mm, the tensile failure criterion was introduced into the finite element simulation process. The results show that the numerical simulation results of the full-scale model and the test results were consistent. The destruction morphology of the target showed severe asymmetry. Under 50 g TNT blast load, the 1.6 mm thick Ti6Al4V titanium alloy target was damaged seriously, and the central area of the target was completely torn. The failure features were mainly petal-shaped warping tearing cracks and localised plastic deformation. The tensile stress is the main stress mode of the target failure. Therefore, dynamic tensile strength should be used as one of the selection criteria for explosion-resistant titanium alloy sheets. The target failure mode is dominated by adiabatic shear fracture.

Largest scale successful real-time evacuation after the Wenchuan earthquake in China: lessons learned from the Zengda gully giant debris flow disaster

A catastrophic debris flow occurred in the Zengda gully, a branch of the Dajinchuan River in Zengda town, Jinchuan County, Sichuan Province, China. The successful implementation of a real-time evacuation avoided 820 casualties for people living in 200 settlements. This was the largest-scale successful real-time evacuation for a debris flow disaster after the Wenchuan earthquake in China. In order to better reveal the causes of the successful real-time evacuation process of the giant debris flow disaster, the characteristics, formation and movement process of the debris flow were studied using multi-temporal remote sensing images, field investigation, laboratory analysis, and empirical formula calculations. It was found that the successful real-time evacuation was possible because of a well-executed monitoring system, timely release of early warning information, a highly effective operation disaster prevention system, and decisive and advanced avoidance. It also transferred strategies through in-depth analysis of several important stages in the real-time evacuation process. Finally, an exemplary mode of community-based warning is proposed based on the Zengda gully giant debris flow disaster real-time evacuation. Specifically, the mode was led by government, implemented by local residents and proceeded with the guidance by experts in the field. The experience and effective risk avoidance mode presented in this paper can be shared and employed by other countries or regions at serious risk for debris flow disasters.

Experimental study on shock wave from dynamic explosion of a warhead based on seismic wave triggering

A method for measuring the shock wave overpressure of blasting warhead explosion based on seismic wave triggering was proposed. By the proposed method, the peak overpressure of the blast wave from dynamic explosion of a warhead can be obtained reliably. The air explosion shock waves of the blasting warhead with the target velocities of 0, 535 and 980 m/s were measured, respectively. And the measured results of the peak overpressure of the shock wave from dynamic explosion of the blasting warhead were compared with those by the empirical formula calculation. The influence of warhead velocity on the pressure field distribution of the shock wave was analyzed quantitatively. Finally, a three-dimensional visualization model for shock wave overpressure from dynamic explosion of the warhead was reconstructed by using the thin-plate-spline interpolation method. The reconstructed model can provide a basis for studying the characteristics of dynamic explosion shock wave based on the measured data in the complex environment of an actual combat.

Dosimetry of pediatric chest X-Ray examinations in Togo

ObjectiveTo assess the entrance surface dose (ESD) of pediatric chest X-ray examinations in order to establish a diagnostic reference levels (DRLs) in Togo. Materials and methodsThe study was carried out in 13 radiology departments within the 6 health regions of the country. This is a descriptive cross-sectional study relating to the dosimetric assessment of the skin of children aged from 0 to 15 years during chest X-ray examinations. The assessment was made by the empirical formula calculation of the entrance surface dose (ESD = 0.15 × (U/100)2 × Q × (1/FSD)2) and with the Internet Dose Calculation Module (MICADO) software online. Statistical assessment was performed using IBM SPSS 21 software. ResultsOur sample numbered 390 with a sex ratio of 1.3 and predominantly male. Examinations performed with the analog radiography units were more irradiating (0.14 mGy) than ones performed with digital detectors (0.12 mGy). The mean dose calculated with MICADO was low (Avg. = 0.12 mGy) compared to that calculated with the theoretical method (Avg. = 0.16 mGy). No significant relationship was found between the professional experience of operators and the entrance surface dose (r > −1 with p = 0.146 not significant). MICADO doses increased with age. The values of the diagnostic reference levels used for the antero-posterior or postero-anterior chest X-ray examinations for children aged 0–1 year; 1–5 years; 5–10 years and 10–15 years were respectively, 0.15 mGy; 0.14 mGy; 0.15 mGy and 0.17 mGy. ConclusionThe entrance surface dose varied greatly from one health facility to another for this same examination. In most of the different age groups of children, the diagnostic reference level was higher than that found in literature. Thus, effective measures must be put in place to optimize the doses delivered to children during chest X-ray examinations.

A Novel Approach for Predicting the Height of Water-Conducting Fracture Zone under the High Overburden Caving Strength Based on Optimized Processes

The height of water-conducting fracture zones (WCFZs) is vital for the prevention of water, gas, and roof accidents in coal mines. However, its dynamic evolution law and maximum height are difficult to be obtained by traditional prediction methods, especially for conditions in which there is high overburden caving strength and a thick coal seam. Therefore, taking the 150,313 fully mechanized caving working face in Yingying Coal Mine as a background, according to the principle of optimized processes, a new predicting approach based on the Brillouin optical time-domain reflectometry (BOTDR) is proposed. Firstly, we estimated the height through empirical formula calculation, theoretical analysis, and similar model simulation tests. Secondly, we studied the optimized layout of optical cables in the overburden in detail for predicting the maximum height of the WCFZ and keeping the cables in good performance during field prediction. Thirdly, we researched and optimized the borehole parameters, optical fiber selection, and the special protection measures. Finally, we applied the aforementioned optimized outcomes in the field experiment to dynamically predict the height of the WCFZ. As a result of the field experiment, the distribution characteristics of optical fiber strain, the maximum height, and the evolution law of the WCFZ were obtained through the regular monitoring of fiber strain using BOTDR. The experiment demonstrated that its maximum height is consistent with the results studied indoors. The validation and feasibility of the approach proposed in this paper were verified via the aforementioned studies. The research in this paper has good reference value and important significance for predicting the height of the WCFZ using BOTDR in coal mines with similar geological and productive conditions.

Design optimization and CFD evaluation of a volute swirl burner with central gas supply

The reasonable design and optimization can be useful tools to solve issues in several industrial applications. Since it is time-consuming and costly to do the experimental performance assessment using various equipments, computational fluid dynamics (CFD) with suitable models has been widely used due to the good agreement with experiments. This paper presented a universal design calculation method of a volute swirl burner with central gas supply. Then, CFD simulations with standard k–e model, under non-reacting and reacting conditions, were carried out to verify the design feasibility. The mixedness of gas/air under non-reacting condition was evaluated from the perspective of normal distribution in statistics and checked by the designed excess air factor. A parametric study for various mixing section lengths and outlet diameters of the burner block was conducted to investigate their influence on the central recirculation zone and the temperature distribution. Simulation results show good agreement with empirical formula calculation. The gas and air have been mixed uniformly around the location that is 60 times of the gas orifice diameter. Additionally, an enlarged recirculation zone with increased recirculation strength can be formed with the increasing mixing length and block outlet diameter. In combustion simulation, the longer mixing length improves the flame stabilization but makes the combustion center move to the upstream of the burner due to the strengthened recirculation zone. The larger outlet diameter of the block stretches the flame and moves the high-temperature zone inside the flame to the downstream of the block wall.

Physical and chemical indexes of synthetic base oils based on a wavelet neural network and genetic algorithm

PurposeThe purpose of this paper is to use the wavelet neural network and genetic algorithm to study the effects of polyalphaolefin, TMP108 and OCP0016 on the kinematic viscosity, viscosity index and pour point of lubricating oil.Design/methodology/approachWavelet neural network is used to train the known samples, test the unknown samples and compare the obtained results with those obtained with a traditional empirical formula.FindingsIt is found that the wavelet neural network prediction value is closer to the experimental value than the traditional empirical formula calculation value.Originality/valueThe results show that the wavelet neural network can be used to study the physical and chemical indexes of lubricating oil.

Neutron penetration in labyrinths under different beam losses

Multiple analytical methods and Monte Carlo simulations were performed to evaluate neutron penetration in straight and curved labyrinths. Factors studied included variations in beam losses of off-axis point source, on-axis point source, and line source. For the straight labyrinth, it was found that the analytical expressions neglect the dose rate platform appearing at the bend of the labyrinth, and the agreement between analytical methods and Monte Carlo estimation was related to the type of neutron source term. For the curved labyrinth, the neutron attenuation length obtained under different conditions was nearly identical and appeared to be in quite good accord with the empirical formula calculation. Moreover, the neutron energy spectra along the centerline distance of the labyrinth were also analyzed. In the first leg, differences in beam loss led to variance in the distribution of spectra, while in the second and subsequent legs, the spectra were similar, where the main contributors were thermal neutrons. This work is valuable for practical design of the labyrinths in the accelerator facilities.

Analysis of Influencing Factors on Noise Reduction Effect of High-Speed Railway Sound Barrier

As an effective and economical noise reduction measure, sound barrier has been widely recognized and applied in the research field of high-speed railway noise reduction. The equivalent sound source height corresponding to the two different sound barrier forms of subgrade and bridge are analyzed by the empirical formula calculation method, and the influencing factors of noise reduction effect of high-speed railway are analyzed. Some referential conclusions is obtained.

Experimental Study of Laminar Cooling Process on Temperature Field of the Heavy Plate

Laminar cooling is the key to hot rolling and controlled cooling. It can improve the performance of steel by changing the grain transformation. The key to improve product quality is that the laminar cooling process model can calculate the cooling strategy accurately. The conventional empirical formula calculation method can’t guarantee the accuracy of the water cooling heat transfer coefficient, which is the critical parameters of laminar cooling process. Therefore, an experimental study like this is needed. In this paper, the temperature measurement experiment of laminar cooling is carried out by the method of experimental temperature measurement. The experimental design stage uses COMSOL software to simulate the temperature field temperature to determine the diameter and depth of the measurement. Then the laminar cooling experiment is carried out and collects the temperature measurement data under different conditions. The error of the measured temperature field is less than 0.1% under the final experimental conditions. The heat transfer coefficient is obtained by experimental data and input in heat transfer model, the surface temperature is calculated, and the temperature is compared with the experimental data, the relative error is less than 20°C.

Research on Experimental Method for Obtaining Independent Combustion Noise of Internal Combustion Engine

Internal combustion engine noise sources are complex and changeable. Combustion noise is usually drowned out by mechanical noise and aerodynamic noise. Traditional noise source identification methods can only qualitatively identify combustion noise. In order to quantitatively obtain the independent pure combustion noise of an internal combustion engine, it is necessary to design and build a separate noise source simulation test bench. In this paper, the combustion noise separation test bench based on transfer function method is designed and implemented. In the test, a pressure pulse device is installed in the combustion chamber. When the piston is at top dead center (TDC), pulse pressure is generated to excite the internal combustion engine to radiate noise. The pressure signal and noise signal are utilized to obtain the transfer function of combustion pressure and noise. Then, according to the cylinder pressure and transfer function, the combustion noise can be directly calculated. The test was carried out on 4120SG diesel engine. Experimental results show that when the internal combustion engine is under 1500 rpm and no-load condition and 800 rpm and no-load condition, the frequency components of independent pure combustion noise are both mainly concentrated at 1100 Hz, 1400 Hz, and 3000 Hz. Furthermore, the internal combustion engine vibration test method and the combustion noise empirical formula calculation method are both carried out to show accuracy and effectiveness of the obtained independent combustion noise through the combustion noise separation test based on transfer function method.