Similarity Theory Research Articles

Rainfall–Mining Coupling Effects on Slope Failure Mechanism and Evolution Process: A Case Study of Open-Pit to Underground Mining

This research examines how rainfall and mining affect the slope damage resulting from the transition from open-pit mining to underground mining. Using an unmanned aerial vehicle (UAV), the Huangniu slope of the Dexing Copper Mine was fully characterized, and experiments were conducted on rock samples from appropriate sites. First, the mechanical properties of the samples were measured. Then, the parameters of the similarity simulation experiments were derived based on the similarity theory. Subsequently, the rainfall, rock slope, data acquisition, and monitoring systems were designed. Finally, the rock mass failure with different slope angles was analyzed, and the deformation and damage patterns under the coupling effect were obtained. The results show that rainfall increases pore water pressure and moisture content. Rainfall and slope-slip water have more of an impact on the open-pit platform. The pore water pressure values on the upper rock mass rise faster than inside it. In the open-pit mining stage, the rock mass shifts slightly to the upper left. In the room mining stage, vertical fractures and goaf sinking occur. The fractures above the mine form a semi-ellipse. In the pillar mining stage, overlying rock displacement is evident and fractures persist. In the continuous pillar mining stage, the overlying rock collapses. The 65° slope model was the most damaged, while the 55° slope model was the least damaged. The results also suggest that the UAV guides sample selection.

Методика циклических испытаний образцов-моделей коленчатого вала судового двигателя внутреннего сгорания на изгиб с кручением

It is proposed to consider the bending fatigue strength of the crankshaft as the main criterion of its operability during operation. It is noted that thermomechanical straightening with heating by stress relaxation method is most acceptable for straightening critical shafts that have received a curvature of the longitudinal axis during operation. Bending fatigue tests of round samples with a diameter of 20 mm in a dangerous section were carried out to substantiate the correction technology, test modes and evaluate the results of the correction. It was found that an increase in diameter leads to a decrease in the endurance limit of structural steels. The loading scheme of the experimental sample is adopted – transverse bending with torsion. A semicircular notch in the sample was used to focus the fracture site, and the radius of the notch was calculated. The size of the sample tuck is determined by the formula based on the similarity criterion adopted in the statistical theory of similarity of fatigue failure of parts, proposed by V. P. Kogaev. The requirements for the roughness of the surface of a circular groove of at least Ra 0.16 are established. The need for control of the manufacturing technology of the experimental sample is noted. An experimental installation for testing flexural fatigue strength is proposed. A cone cartridge was used to securely fasten and prevent the sample from turning during the experiment. Experimental samples were used-models with deflection arrows of 1, 2, 3, 4 and 5 mm. The method and equipment for obtaining samples with the necessary deflection arrows have been determined. Diagrams of a model sample for testing cantilever bending with torsion, an experimental installation for testing model samples, bending to a given deflection arrow, and a model sample with a curved longitudinal axis are presented.

Advancing real-time error correction of flood forecasting based on the hydrologic similarity theory and machine learning techniques

Real-time flood forecasting is one of the most pivotal measures for flood management, and real-time error correction is a critical step to guarantee the reliability of forecasting results. However, it is still challenging to develop a robust error correction technique due to the limited cognitions of catchment mechanisms and multi-source errors across hydrological modeling. In this study, we proposed a hydrologic similarity-based correction (HSBC) framework, which hybridizes hydrological modeling and multiple machine learning algorithms to advance the error correction of real-time flood forecasting. This framework can quickly and accurately retrieve similar historical simulation errors for different types of real-time floods by integrating clustering, supervised classification, and similarity retrieval methods. The simulation errors “carried” by similar historical floods are extracted to update the real-time forecasting results. Here, combining the Xin'anjiang model-based forecasting platform with k-means, K-nearest neighbor (KNN), and embedding based subsequences matching (EBSM) method, we constructed the HSBC framework and applied it to China's Dufengkeng Basin. Three schemes, including “non-corrected” (scheme 1), “auto-regressive (AR) corrected” (scheme 2), and “HSBC corrected” (scheme 3), were built for comparison purpose. The results indicated the following: 1) the proposed framework can successfully retrieval similar simulation errors with a considerable retrieval accuracy (2.79) and time consumption (228.18 s). 2) four evaluation metrics indicated that the HSBC-based scheme 3 performed much better than the AR-based scheme 2 in terms of both the whole flood process and the peak discharge; 3) the proposed framework overcame the shortcoming of the AR model that have poor correction for the flood peaks and can provide more significant correction for the floods with bad forecasting performance. Overall, the HSBC framework demonstrates the advancement of benefiting the real-time error correction from hydrologic similarity theory and provides a novel methodological alternative for flood control and water management in wider areas.

Seismic performance of a frame‐supported shear wall over‐track building through shaking table test

SummaryThis research deals with a frame‐supported shear wall for urban over‐track building of vehicle depot in Chisha, Guangzhou, China, which is characterized by its remarkable height of 160.8 m. Technical issues are commonly encountered in these kinds of buildings due to discontinuous vertical structural rigidity, large podium, and structural transition. These challenges significantly impact the engineering process, especially when the rigidity difference between transfer story exceeding the threefold, as well as the building height exceeds limit as in code. In this paper, a shaking table test was developed based on a 1:10 scaled model of the structure. Using similarity theory, the dynamic similarity relationship was established for the design of the model. Subsequently, the experimental model was constructed with the configuration of critical parameters such as mass design, sensor placement, and seismic test conditions. This was followed by in‐depth analysis, recording component failures and investigating key aspects such as dynamic characteristics, that is, acceleration and displacement responses and shear force distribution under different earthquake intensities. A theoretical seismic response of the prototype structure was derived from the test results. The shaking table tests confirmed that the structure met the stringent seismic design requirements as prescribed in the Chinese standards, with no damage under minor earthquakes, repairability under moderate earthquakes, and collapse prevention under rare earthquakes. The results of the study provide valuable insights along with improvement measures for the design and development of similar urban over‐track buildings, potentially contributing to more efficient land use in urban China.

Research on the ratio of similar materials in water-absorbent mudstone based on fuzzy mathematics.

To determine the suitability and credibility of similar water-absorbent mudstone materials in model experiments, the prototype mudstone parameter similarity index was determined based on the similarity theory. Similar materials use cement and Plaster as binders and quartz sand as aggregate. The sensitivity of similar indicators of similar materials to control factors was analyzed through range statistics. Multiple regression analysis was used to establish the quantitative relationship between each control factor and similar indicators. Finally, the optimal matching scheme was refined through the combination of fuzzy mathematics and analytic hierarchy process. The results show that the physical and mechanical property indicators of similar materials with different proportions have a wide distribution range, and under certain similar conditions, they can meet the requirements of rock model tests with different properties. The aggregate-binder ratio is a direct indicator of material density, elastic modulus, and compressive strength. The main controlling factors, material density, elastic modulus, and compressive strength all increase with the decrease in aggregate-binder ratio. The cement-plaster ratio is the main control factor of material water absorption, and the water absorption gradually decreases with the increase of the cement-plaster ratio. The formula obtained through linear analysis can better represent the changing trend and distribution characteristics of various parameters of similar materials with the aggregate-binder ratio and cement-plaster ratio, and initially optimize the proportioning scheme of similar materials. Use fuzzy mathematics to evaluate the membership degree of each parameter index of similar materials, and the optimal ratio scheme was further determined to improve the credibility of later model experiments.

A supplier selection method based on cobweb similarity and prospect theory for prefabricated components

Selecting suppliers for prefabricated components (PCs) involves a complex decision-making process, frequently relying on ambiguous information and subjective judgment. However, most existing methods use precise values to portray indicator information and overlook the uncertainty of weights and the subjective preferences of decision-makers (DMs). In order to address these limits, this paper proposes a novel approach to select suppliers of PCs. Initially, an evaluation index system for suppliers is established through literature analysis and a questionnaire survey. The system comprises six layers: product quality, price, service level, comprehensive ability, supply ability, and environmental sustainability. The group decision matrix is then constructed using the set-valued statistical method and the prospect theory. The index weights are determined by a combination weighting method. Next, the cobweb model is introduced to analyze the disparity between the alternative and ideal solutions, describing their similarities in terms of area and shape. Lastly, cobweb similarity is employed instead of comprehensive distance, combined with the minimum sum of squares criterion, to improve the closeness algorithm and contrast the alternatives. The results demonstrate that this method facilitates a comprehensive evaluation of the benefits and drawbacks of various alternatives from diverse perspectives. Furthermore, it allows flexible adjustments based on the risk preferences of DMs, ensuring accurate and reliable decision results.

Research examining a spatial autocorrelation imaging method based on stationary characteristics of microtremors

The spatial autocorrelation method is an important method for extracting the velocity dispersion curve from microtremor data. However, site data typically cannot strictly meet spatial and temporal stationary feature, and this greatly affects the accuracy of the calculation results of this method. Therefore, based on the cosine similarity theory, this study deduces the applicability of the spatial autocorrelation method to unidirectional Rayleigh surface waves and again verifies the applicability of this method to spatially and temporally stationary Rayleigh waves. The numerical simulation results demonstrate that the velocity dispersion curve can be extracted from a one-way Rayleigh wave using the spatial autocorrelation method to obtain an accurate geological profile, whereas the superposition of finite groups of Rayleigh waves in different directions cannot yield an accurate geological profile. In this study, we quantitatively analyzed the impact of the spatial autocorrelation method on the extraction of the velocity dispersion curve when the signal could not meet the characteristics of temporal and spatial stationarity through numerical simulation. The results reveal that the velocity-dispersion curve can be accurately extracted only when the signal satisfies both spatial and temporal stationarity. When a signal is closer to the spatial and temporal stationary characteristics, this indicates that a more accurate velocity dispersion curve can be extracted. These results provide a reference for improving the calculation accuracy of spatial autocorrelation methods.

An empirical study of the influences of gustiness on vertical mixing at the air-sea boundary

The exchange of momentum across the air-sea interface is a key driver of the earth system and its accurate parameterization is essential for precise weather and climate forecasting. However, our understanding of gustiness as an independent factor that can contribute to the momentum flux is limited. Using data collected from the R/P FLIP, as part of the Couple Air-Sea Processes and Electromagnetic ducting Research (CASPER) experiment, we explored the mechanisms by which gustiness contributes to the total interfacial momentum flux. We investigate how gustiness affects both the temporal and spatial (vertical) variance of turbulence in the atmospheric surface layer and show that high gustiness was associated with strong anisotropic turbulence at each measurement height. This was found to increase vertical wind fluctuations and inject additional momentum across the air-sea interface at lower wind speeds. Increased gustiness was also associated with the breakdown of the constant flux layer, which is generally assumed to exist over the ocean. This study has implications for both momentum flux parameterization and the use of similarity theory to model the flux-gradient relationship in the gusty atmospheric surface layer, thereby influencing the forecasting of climate and weather.

Hydrodynamic instabilities in a two-dimensional sheet of microswimmers embedded in a three-dimensional fluid

A collection of microswimmers immersed in an incompressible fluid is characterised by strong interactions due to the long-range nature of the hydrodynamic fields generated by individual organisms. As a result, suspensions of rear-actuated ‘pusher’ swimmers such as bacteria exhibit a collective motion state often referred to as ‘bacterial turbulence’, characterised by large-scale chaotic flows. The onset of collective motion in pusher suspensions is classically understood within the framework of mean-field kinetic theories for dipolar swimmers. In bulk two and three dimensions, the theory predicts that the instability leading to bacterial turbulence is due to mutual swimmer reorientation and sets in at the largest length scale available to the suspension. Here, we construct a similar kinetic theory for the case of a dipolar microswimmer suspension restricted to a two-dimensional plane embedded in a three-dimensional incompressible fluid. This setting qualitatively mimics the effect of swimming close to a two-dimensional interface. We show that the in-plane flow fields are effectively compressible in spite of the incompressibility of the three-dimensional bulk fluid, and that microswimmers on average act as sources (pushers) or sinks (pullers). We analyse the stability of the homogeneous and isotropic state, and find two types of instability that are qualitatively different from the bulk, three-dimensional case: first, we show that the analogue of the orientational pusher instability leading to bacterial turbulence in bulk systems instead occurs at the smallest length scale available to the system. Second, an instability associated with density variations arises in puller suspensions as a generic consequence of the effective in-plane compressibility. Given these qualitative differences with respect to the standard bulk setting, we conclude that confinement can have a crucial role in determining the collective behaviour of microswimmer suspensions.

Classical and local similarity in problems of turbulent convection: Extension of Prandtl semi-empirical theory for horizontal layers of water and air mediums

A variant of the local similarity theory is considered, assuming a priori specification of two basic dimensional parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. Such selection of basic parameters lets us interpret the algebraic formulas of Prandtl's semiempirical turbulence theory for the coefficients of turbulent heat transfer and kinetic energy dissipation as relationships of the local similarity theory. A priori approximations of the basic parameters are based on known relationships and consider the upper boundary of the convective layer as a solid wall. Within the framework of local similarity theory, approximations for the turbulent moments of buoyancy and vertical velocity of arbitrary order are also proposed. The correspondence of these approximations to experimental data has been established in both air and water mediums, as well as in the results of numerical modeling. Such correspondence allows us to conclude that a wide class of vertical profiles of turbulent moments in a windless convective layer depends only on two basic parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. The obtained result indicates the universal nature of the theory of local similarity and is a significant addition to the semiempirical Prandtl theory.

A Novel Similarity Approach for Describing the Bulk Shear in the Atmospheric Surface Layer

The Monin–Obukhov Similarity Theory (MOST) is a cornerstone of boundary layer meteorology and the basis of most parameterizations of the atmospheric surface layer. Due to its significance for observations and modelling, we generalize the dimensional analysis of MOST by considering the bulk gradient directly, enabling the study of any sublayer of the atmospheric surface layer. This results in a family of similarity relations describing all gradients from the local gradient to the full-layer bulk gradient. By applying the profiles derived from the law-of-the-wall and MOST, we are able to derive analytic expressions for this family of similarity relations. Under stable conditions, we discover that the log-linear profile of Businger–Dyer generalizes from the local to the bulk shear where the slope is dependent on the choice of the layer. The simplicity of the general log-linear relation allows for estimating the influence of stability on the non-dimensional gradients. It is shown that bulk gradients are less sensitive to stability than the local gradient. By correctly filtering cases where the full-layer bulk gradient is influenced by stability, we demonstrate that MOST is compatible with the Hockey-Stick Transition. For unstable conditions, the Kader and Yaglom (J Fluid Mech 212(151):637-662, 1990) model represents the local gradient well but was not successful in representing the bulk gradient, demonstrating the need for further analysis of scaling relations for the unstable atmospheric surface layer.

An Investigation of LES Wall Modeling for Rayleigh–Bénard Convection via Interpretable and Physics-Aware Feedforward Neural Networks with DNS

Abstract The traditional approach of using the Monin–Obukhov similarity theory (MOST) to model near-surface processes in large-eddy simulations (LESs) can lead to significant errors in natural convection. In this study, we propose an alternative approach based on feedforward neural networks (FNNs) trained on output from direct numerical simulation (DNS). To evaluate the performance, we conduct both a priori and a posteriori tests. In the a priori (offline) tests, we compare the statistics of the surface shear stress and heat flux, computed from filtered DNS input variables, to the stress and flux obtained from the filtered DNS. Additionally, we investigate the importance of various input features using the Shapley additive explanations value and the conditional average of the filter grid cells. In the a posteriori (online) tests, we implement the trained models in the System for Atmospheric Modeling (SAM) LES and compare the LES-generated surface shear stress and heat flux with those in the DNS. Our findings reveal that vertical velocity, a traditionally overlooked flow quantity, is one of the most important input features for determining the wall fluxes. Increasing the number of input features improves the a priori test results but does not always improve the model performance in the a posteriori tests because of the differences in input variables between the LES and DNS. Last, we show that physics-aware FNN models trained with logarithmic and scaled parameters can well extrapolate to more intense convection scenarios than in the training dataset, whereas those trained with primitive flow quantities cannot. Significance Statement The traditional near-surface turbulence model, based on a shear-dominated boundary layer flow, does not represent near-surface turbulence in natural convection. Using a feedforward neural network (FNN), we can construct a more accurate model that better represents the near-surface turbulence in various flows and reveals previously overlooked controlling factors and process interactions. Our study shows that the FNN-generated models outperform the traditional model and highlight the importance of the near-surface vertical velocity. Furthermore, the physics-aware FNN models exhibit the potential to extrapolate to convective flows of various intensities beyond the range of the training dataset, suggesting their broader applicability for more accurate modeling of near-surface turbulence.

Experimental and Numerical Analysis of Concrete Columns under Axial Load Based on European Design Norms

This study presents a comparison between numerical and experimental results for reinforced concrete columns subjected to axial compression. Depending on the columns support and their organization within the structure, columns primarily work under either concentric or eccentric compression, respectively, bending in situations where horizontal actions such as wind or/and earthquakes are present in the structure. Different countries have specific design codes, and in this study, the calculation of columns is based on the European design codes, specifically EN 1992-1-1. As a common practice in most cases during research, tests are conducted using computational models, and based on the obtained results through the application of similarity theory, an attempt is made to transition to the actual behavior of structural elements. Therefore, this paper applies a logic of "almost real" testing, where two columns with square cross-sections were produced and tested. The columns had a rectangular base with cross-section dimensions of 20/20 cm and a height (L) of 300 cm, with a concrete strength of fcm,cube=61.80 MPa. They were reinforced with longitudinal reinforcement (4Ø12 mm) and had a tensile strength of ftm=588.10 MPa. Additionally, stirrups of Ø8 mm were placed at every sw=25 cm. Experimental results show a closer alignment with software calculations using SEISMOSOFT with an accuracy of 96%, while results according to EN 1992-1-1, based on simplified methods, show 64% for the Nominal Stiffness Method and 59% for the Curvature Method. Doi: 10.28991/CEJ-2024-010-02-05 Full Text: PDF

Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

Whole-school interventions promoting student commitment to school to prevent substance use and violence, and improve educational attainment: a systematic review.

Whole-school interventions modify the school environment to promote health. A subset of these interventions promotes student commitment to school to prevent substance (tobacco, alcohol, other drugs) use and/or violence. A previous review identified the theory of human functioning and school organisation as a comprehensive theory of such interventions, and found evidence that these interventions reduce substance use and/or violence. The objectives were to search for, appraise and synthesise evidence to address the following questions: (1) What whole-school interventions promoting student commitment to school to prevent substance use and/or violence have been evaluated, what intervention subtypes are apparent and how closely do these align with the theory of human functioning and school organisation? (2) What factors relating to setting, population and intervention affect implementation? (3) What are the effects on student substance use, violence and educational attainment? (4) What is the cost-effectiveness of such interventions? (5) Are intervention effects mediated by student commitment to school or moderated by setting or population? A total of 56 information sources were searched (in January 2020), then an updated search of 48 of these was carried out (in May 2021). Reference lists were also searched and experts were contacted. Eligible studies were process/outcome evaluations of whole-school interventions to reduce student violence or substance use among students aged 5-18 years attending schools, via actions aligning with the theory of human functioning and school organisation: modifying teaching to increase engagement, enhancing student-staff relationships, revising school policies, encouraging volunteering or increasing parental involvement. Data extraction and quality assessments used existing tools. Theory and process reports were synthesised qualitatively. Outcome and economic data were synthesised narratively; outcome data were meta-analysed. Searches retrieved 63 eligible reports on 27 studies of 22 interventions. We identified four intervention subtypes focused on student participation in school-wide decisions, improving staff-student relationships, increasing engagement in learning and involving parents. The theories of change of most intervention subtypes aligned closely with the theory of human functioning and school organisation, and informed refinement of an intervention theory of change. Theories of change for interventions increasing learning engagement did not align with this theory, aiming instead to increase school commitment primarily via social skills curricula. Factors influencing the implementation included whether or not interventions were tailorable, workable and well explained. Interventions with action groups comprising staff/students, etc. and providing local data were well implemented. Implementation was also affected by whether or not schools accepted the need for change and staff had the resources for delivery. Meta-analyses suggest small, but significant, intervention effects in preventing violence victimisation and perpetration, and substance use. There was sparse and inconsistent evidence of moderation and some evidence of mediation by student commitment to school. Two economic evaluations suggested that there is the potential for the interventions to be cost-effective. The quality of the studies was variable and the economic synthesis was limited to two studies. Whole-school interventions aiming to promote student commitment to school share similar theories of change and factors affecting implementation. They have the potential to contribute to preventing violence and substance use among young people. Future trials should aim to optimise intervention effectiveness by better theorisation, and assess implementation and effect moderators and mediators. This study is registered as PROSPERO CRD42019154334. This award was funded by the National Institute for Health and Care Research (NIHR) Public Health Research programme (NIHR award ref: 17/151/05) and is published in full in Public Health Research; Vol. 12, No. 2. See the NIHR Funding and Awards website for further award information.

The penetration resistance behavior and corresponding size effects of ultra-high molecular weight polyethylene composite laminates

Focusing on the energy absorption characteristics of ultra-high molecular weight polyethylene (UHMWPE) fiber laminated panels, this study conducts ballistic tests and numerical simulations using 6 mm spherical projectiles to impact the UHMWPE laminated panels. The residual velocity characteristics, energy absorption patterns, and failure modes of the UHMWPE laminated panels under steel ball impacts were analyzed. The results show that the residual velocity of the steel ball increases with the increase of the incident velocity. In the velocity range near the ballistic limit velocity, the residual velocity of the steel ball increases sharply. When the incident velocity exceeds 340 m/s, the increase in residual velocity gradually slows down, tending towards a straight line. When the steel ball velocity is less than 330 m/s, the energy absorption of the UHMWPE laminated panels exhibits linear growth with increasing velocity, with a maximum energy absorption of 47.3 J. In the 327–340 m/s velocity range, the energy absorption of the laminated panels drops sharply from 47 J to around 30 J. In the 340 m/s–600 m/s velocity range, the decline in energy absorption gradually becomes more moderate, decreasing to around 20 J. Beyond 500 m/s, the energy absorbed by the UHMWPE laminated panels stabilizes with increasing velocity, and the fiber tensile failure is the main form of energy absorption of UHMWPE composite laminates under ballistic impact. The failure process of UHMWPE laminated panels presents a multi-stage failure mode, including fiber shear failure, tensile failure, and delamination. As the projectile’s incident velocity increases, the damage mechanism of the UHMWPE laminated panels transitions from tensile-dominated to shear plugging-dominated. Through similarity theory analysis, under certain conditions, the ballistic limit velocity and the dimensionless parameter of unit energy absorption for the UHMWPE laminated panels satisfy geometric similarity.

Short-term photovoltaic output power prediction based on similar day and optimized BP neural network

Abstract The photovoltaic (PV) output power is affected by the ambient temperature, seasons, weather and other factors, which makes the PV output power very unstable. Therefore, accurate prediction of the PV output power is highly beneficial. This paper is dedicated to finding a simple and reliable PV short-term output power prediction method. First, we choose four key parameters, season, solar irradiance, temperature and relative humidity, to predict PV output power by using the similar day theory, which is mainly because the above four parameters are decisive for PV output power, although more parameters being taken into account will make the prediction accuracy higher, but it brings along with it an increase in the complexity; secondly, we choose the backpropagation (BP) neural network because it is very suitable for the PV output power prediction due to its excellent learning ability; finally, we optimize the standard BP neural network in loss functions, activation functions and optimizers to further improve its prediction accuracy. We validate the proposed method in different seasons and under other weather conditions. The results show that the proposed method has better prediction results, the optimized BP neural network has better performance compared with the standard BP neural network, and the standard deviation of the prediction is improved from ~1382, ~1571, ~1457, ~989 to ~903, ~792, ~333 and ~409.

Features of calculating the temperature field in an annular porous layer under infinite heating

To date, easily recoverable oil reserves have already been extracted, so deposits with residual oil reserves or places with weak permeability are of great interest. It is known that oil becomes more viscous when the temperature decreases, which creates difficulties in its production. Therefore, to reduce the viscosity, it is necessary to heat the oil to the temperature at which it is possible to realize its production. The study proposes a mathematical model for calculating the temperature field in an annular porous layer under infinite heating in a downhole reactor for continuous heating of the bottom-hole zone of a formation containing high-viscosity oil and natural bitumen (HVO and NB).PURPOSE. To construct a heating solution for an infinitely long annular layer in a downhole reactor. To obtain a temperature profile in the cross section of the annular layer and a picture of the temperature field.METHODS. The equations of the mathematical model are based on the laws of conservation of energy and mass, their study and evaluation are carried out using analytical methods of the theory of differential equations, methods of similarity theory and dimensions, as well as numerical methods for solving boundary value problems. results. In the course of the study, the dependences of the distance at which the set air temperature in the reactor is reached at different values of mass air flow, linear heat flux density and the heat capacity of the mixture were obtained. conclusion. The conducted studies have allowed us to obtain a mathematical model for calculating the temperature field in an annular porous layer under infinite heating in an downhole reactor. The results obtained showed that with an increase in the mass flow rate and the heat capacity of the medium, the distance at which the set air temperature in the reactor is reached increases by 1.6 and 1.5 times, respectively, over the entire temperature range, and with an increase in the linear density of the heat flux, this distance decreases by 0.6 times.

Large-eddy-model closure and simulation of turbulent flux patterns over oasis surface

Abstract. Large-eddy simulations (LESs) have been increasingly used for studying atmosphere and land surface interactions over heterogeneous areas. However, parameterizations based on Monin–Obukhov Similarity Theory (MOST) often violate the basic assumptions of the very theory, generate inconsistencies with the LES turbulence closures, and produce surface flux estimates depending on LES model resolutions. Here, we propose a novel scheme for turbulent flux estimates in LES models. It computes the fluxes locally using the LES subgrid closure, which is then constrained on the macroscopic scale using MOST. Compared with several other schemes, the new scheme performs better for the various types of land surfaces tested. We validate our scheme by comparing surface flux estimates with field measurements obtained over an oasis surface at various height levels. Additionally, we scrutinize other quantities related to the surface energy balance, including net radiation, ground heat flux, and surface skin temperature, all of which align well with observational data. Our sensitivity experiments, focusing on model horizontal resolution, underscore the robustness of our scheme, as it maintains its corrective efficacy despite changes in horizontal grid spacing. We find that the macroscopic constraint imposed by MOST on LES-estimated fluxes strengthens as the horizontal grid spacing decreases, with a more pronounced influence on sensible than latent heat fluxes. These findings collectively highlight the promise and adaptability of our scheme for improved surface flux estimates in LES models.

The effect of micro-gap discharge paths on ionization coefficients and similarity theory

In order to investigate the impact of discharge paths at the micrometer scale on breakdown, two sets of different electrodes were arranged with electrode gaps ranging from 10 μm to 100 μm and gas pressures varying from 1 kPa to 100 kPa. The research has revealed that without an insulating layer at the edge of the electrode, when the product of gas pressure (p) and electrode gap (d) is less than 60Pa·cm, the number of positive ions cannot satisfy the conditions for self-sustaining discharge at the electrode gap (d). As a result, the discharge path varies along a longer path (s) to satisfy the conditions for self-sustained discharge, thereby maintaining the minimum breakdown voltage. This long-path discharge mechanism affects the ionization coefficient, resulting in an inconsistency between the ionization coefficient ratio at different distances and their respective scale factor (k) values. Therefore, on a micrometer scale, changes in the path make the application of similarity theory no longer applicable.