Equations Of Mathematical Model Research Articles

Modeling and solution of eigenvalue problems of laminated cylindrical shells consisting of nanocomposite plies in thermal environments

AbstractThis work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.

Ibuprofen Release from Poly(L-Lactic Acid)/Cellulose Blend Tablets: Box-Behnken Design for Optimization of the Influenced Parameters

According to the literature, blending PLA with cellulose, a natural polymer, can improve their use in the field of drug delivery systems. This work aimed to prepare a ternary mixture of ibuprofen, poly(L-lactic acid) (PLLA), and cellulose by the physical mixing method and to determine the effect of three selected factors (PLLA/cellulose blend ratio, percentage of the blend, and time of contact) on the amount of IBF released as a function of time. A Box-Behnken experimental design created using Minitab 17 software was used to study and optimize the selected factors. The percentage of IBF released significantly decreased with increasing PLLA/cellulose blend ratio (X1) and percentage of blend (X2). No significant interactions between the three factors were observed for Y1 (30 minutes), Y2 (60 minutes), and Y3 (120 minutes). A significant interaction between the PLLA/ cellulose ratio and the percentage of the blend was observed only for Y4 (180 minutes). ANOVA revealed that the refined mathematical model equations for Y1, Y3, and Y4 were more adequate than Y2 to explain the investigated total variations

Evaluation of Wear Model Equations Through Analysis of Experimental Wear Data of Materials from Literature

Understanding the correlation between material characteristics and wear behavior helps in the development and manufacturing of high-quality materials for components subjected to wear, like brake pads, bearings etc. The majority of published research papers present experimental data from pin-on-disc experiments in which wear volume loss is measured using wear rate and sliding distance. However, in many publications pin on disc experimental data is interpreted by statistical methods like Taguchi method to understand the effect of material characteristics on wear behavior. This method indirectly correlates wear behavior to material parameters like hardness, modulus of elasticity and toughness of the material. However, many mathematical models are proposed in literature to directly relate material characteristics to wear behavior. However, there are gaps in published literature in interpretation of experimental data with mathematical model equations. The mathematical models like Archard model, Evans and Wilshaw model, Kato model etc proposed in literature are defined to link material characteristics like modulus of elasticity, hardness, toughness etc to wear behavior. In this study, it is proposed a methodology to interpret the pin on disc experimental wear data by fitting an analytical model to understand effect of material characteristics on wear behavior of materials.

On the representation of multiplicative noise in modeling Dansgaard–Oeschger events

The interpretation of multiplicative noise in a stochastic differential equation in the context of data-driven inverse modeling is discussed. Application to the well-known paleoclimate phenomenon of Dansgaard–Oeschger events leads to qualitatively different ‘climate potentials’ in the case of the Itô or the Stratonovich interpretation of the stochastic integral. While a physical model is endowed with an interpretation from construction, whether implicitly or explicitly, inverse models derived from data do not afford such a luxury. In this case, a physical model must accompany the mathematical model equation in order to be able to choose a stochastic interpretation. This case study illustrates the differences between the two representations of stochastic noise and demonstrates the need for input from physical constraints when constructing conceptual stochastic models of the observed climate records.

Design and time-domain finite element simulation of multi-functional transformation optical device

In this paper, we first proposed mathematical model equations for wave propagation in a multi-functional transformation optical device, namely, an electromagnetic rotation concentrator. This device can concentrate electromagnetic energy while rotating electromagnetic waves. We also demonstrate the stability of the model equation in the continuous case. Next, we designed the multi-functional device with multiple layers. We then proposed a time-domain finite element method for simulating wave propagation in this device and conducted a stability analysis of the model equations in the discrete case. Finally, we implemented the proposed algorithm and obtained numerous numerical results that demonstrate the validity of our model equations. To the best of our knowledge, this is the first work on time-domain modeling and analysis of multi-functional electromagnetic devices.

Enhancing the Permeate Flux Improvement of Direct Contact Membrane Distillation Modules with Inserted S-Ribs Carbon-Fiber Filaments.

Three widths of manufacturing S-ribs carbon-fiber filaments acting as turbulence promoters were implemented into the flow channel of direct contact membrane distillation (DCMD) modules to augment the permeate flux improvement in the present study. Attempts to reduce the disadvantageous temperature polarization effect were made by inserting S-ribs turbulence promoters in improving pure water productivity, in which both heat- and mass-transfer boundary layers were diminished due to creating vortices in the flow pattern and increasing turbulence intensity. The temperature polarization coefficient ttemp was studied and found to enhance device performance (less thermal resistance) under inserting various S-ribs carbon-fiber thicknesses and operating both cocurrent- and countercurrent-flow patterns. The permeate fluxes in the DCMD modules with inserted S-ribs carbon-fiber turbulence promoters were investigated theoretically by developing the mathematical modeling equations and were conducted experimentally with various design and operating parameters. The theoretical predictions and experimental results exhibited a great potential to considerably achieve permeate flux enhancement in the new design of the DCMD system. The DCMD module with inserted S-ribs carbon-fiber turbulence promoters in the flow channel could provide a relative permeate flux enhancement up to 37.77% under countercurrent-flow operations in comparisons with the module of using the empty channel. An economic consideration on both permeate flux enhancement and power consumption increment for the module with inserted S-ribs carbon-fiber filaments was also delineated.

GIS-based determination of potential snow avalanche areas: A case study of Rize Province of Türkiye

Natural hazards are a part of critical issues affecting people and the environment. One of these natural hazards is snow avalanches. With the increase in the world population, it has emerged that decision-makers should take precautions against such natural hazards for population movements, construction, transportation, and tourism. Essential solution parts of this problem lay behind surveying, GIS, and spatial analysis-planning. This situation will be primarily due to the snow conditions, but certain terrain areas are susceptible. Snow avalanches' release mechanism depends on many factors, such as terrain, meteorological reports, snowpack, and other triggering parameters. Areas with certain topographical features that allow the deposition of snow masses are called avalanche-release areas. GIS helps to make decisions concerning spatial planning within avalanche release areas and finding risky zones. This study aimed to determine the potential avalanche release areas in the GIS environment in Rize, Türkiye, which was chosen as the pilot region. In the study, the detection of these avalanche areas was estimated using a mathematical equation model proposed by Hreško (1998) and determined with the help of GIS. Factors such as elevation, curvature, aspect, slope, and land cover type were used to estimate avalanche risk areas. A Model Builder workflow has also been created to automate the process stages. As a result of the study, avalanche risk areas were determined and mapped for the Rize mountainous region.

Entropy generation and heat transfer analysis of Eyring-Powell nanofluid flow through inclined microchannel subjected to magnetohydrodynamics and heat generation

The current study is inspired to investigate the influences of essential flow dynamics including magnetic field, variable dynamic viscosity, Joule heating, viscous dissipation, porous medium dissipation, heat source, thermal radiation, and convective heating on the mixed convection flow of Eyring-Powell Cu − water nanofluid trough an inclined microchannel in the presence of Darcy-Forchheimer porous medium. The governing mathematical model equations are formulated, converted into dimensionless and thereafter solved numerically in the MATLAB software via Bvp4c-package. The influences of the embedded dimensionless parameters on heat transfer behaviours and entropy generations are displayed trough graphs as well as their physical interpretations are discussed in detail. Consequently, it is revealed that the performance of microchannel thermal system is improved by factors such as injection/suction of fluids, Eyring-Powell fluid, magnetic field, non-Darcy porous medium, Cu − nanoparticles, thermal radiation and convective heating. The drag coefficient and Nusselt number augment with viscous dissipation, variable dynamic viscosity, Darcy porous medium, angle of inclination, Prandtl number and heat source. Moreover, the Nusselt number at around the left and right walls vicinity shows an opposite behaviour with escalating values of the Biot number and thus convective transfer of heat around the microchannel walls is remarkably important. Furthermore, the minimization of net entropy generation rate is achieved with Eyring-Powell fluid, magnetic field, Cu − nanoparticles, thermal radiation and convective heating but it escalates with variable dynamic viscosity, viscous dissipation, angle of inclination, heat source and Prandtl number. Indeed, the irreversibility due to the robust influence of porous medium shows dual behaviours on the net entropy generation rate. Finally, the numerical results are also validated by comparing with the results of already existing literatures and hence, a sounding agreement is attained.

CMISR: Circular medical image super-resolution

Classical methods of medical image super-resolution (MISR) utilize open-loop architecture with implicit under-resolution (UR) unit and explicit super-resolution (SR) unit. The UR unit can always be given, assumed, or estimated, while the SR unit is elaborately designed according to various SR algorithms. The closed-loop feedback mechanism is widely employed in current MISR approaches and can efficiently improve their performance. The feedback mechanism may be divided into two categories: local feedback and global feedback. Therefore, this paper proposes a global feedback-based closed-cycle framework, circular MISR (CMISR), with unambiguous UR and advanced SR elements. Mathematical model and closed-loop equation of CMISR are built. Mathematical proof with Taylor-series approximation indicates that CMISR has zero recovery error in steady-state. In addition, CMISR holds plug-and-play characteristic that fuses model-based and learning-based approaches and can be established on any existing MISR algorithms. Five CMISR algorithms are respectively proposed based on the state-of-the-art open-loop MISR algorithms. Experimental results with three scale factors and on three open medical image datasets show that CMISR is superior to MISR in reconstruction performance and is particularly suited to medical images with strong edges or intense contrast.

A dynamic simulation study of temperature and humidity independent control system for temperate semi-humid continental monsoon climate regions

A temperature and humidity independent control (THIC) system is a promising solution for hot and humid indoor working environments. This study proposes a dual-source heat pump air-conditioning (DSHPAC) system composed of a dual-source heat pump (DSHP) and air handling unit (AHU) as a THIC system. The proposed THIC system indirectly adjusts the cooling capacity of the high-temperature evaporator (Eva1) and low-temperature evaporator (Eva2) by controlling the refrigerant mass flow rate of the system to meet the cooling and dehumidifying requirements under different operational conditions. The proposed THIC system can switch among three operational modes by using the designed operational strategy, ensuring that the requirements for indoor temperature and humidity are met. In addition, the mathematical model and equilibrium equations of the THIC system are established. This study uses an office building in Xi'an on a typical summer day as a simulation case in dynamic simulations. The coefficient of performance (COP), cooling capacity, and compressor power consumption of the proposed DSHP system are analyzed. The results demonstrate that the COP of the proposed system increases with the temperature of Eva1 (TEva1), the COP of the proposed system varies from 1.76 to 3.62, and the cooling capacity increases from 1.19 kW to 3.38 kW when TEva1 increases from 6.24 °C to 36.4 °C. The analysis of different values of φR (refrigerant mass ratio) shows that the highest COP is achieved at φR = 0.1. The results prove the application potential of the dual-source heat pumps to the THIC air-conditioning systems.

NUMERICAL ANALYSIS IN ARTERIAL STENOSIS AFFECTED BY ISCHEMIC HEART DISEASE USING FINITE VOLUME METHOD

Atherosclerosis is the narrowing of blood vessels caused by the buildup of cholesterol plaque on the walls of the arteries. Excessive buildup of cholesterol plaque disrupts the circulatory system, thereby affecting the speed and pressure of blood flow. In the long term, atherosclerosis can cause ischemic heart disease. This study aims to analyze the influence of stenosis, initial velocity, and diameter on the velocity and pressure of blood flow in narrowed arteries that cause ischemic heart disease. In this research, a Navier Stoke mathematical equation model was built which was solved using the finite volume method with SIMPLE discretization (Semi Implicit Method for Pressure Linked Equations). Finite volume methods are used to analyze unstructured objects such as blood flow. SIMPLE discretization is implemented simply in two and three dimensions with a system of equations containing fluid motion. Matlab and Fluent are software used for process simulations, Matlab for visualizing graphs of numerical calculation results, and Fluent for visualizing blood flow. Based on the simulation results, it can be concluded that the smaller the diameter, the greater the stenosis, and the greater the initial velocity, the greater the blood flow velocity. On the contrary, the diameter gets smaller, the stenosis gets bigger, and the initial velocity gets bigger so that the pressure on the blood flow gets smaller. Blood flow simulation has the potential to contain ischemic heart disease if the maximum speed produced is greater than the maximum normal blood speed, namely 0.45 m/s.

Estimating of radiation output of X-RAY tube using mathematical model: Case of high-frequency machines

PurposeDuring any radiological procedure, it is important to know the dose to be-administered to the patient and this can be done by estimating the output of the X-ray tube either with a dosimeter or with a mathematical equation or Monte Carlo simulations. The aim of this work is to develop a new mathematical model equation (NMME) for estimating the output of high-frequency X-ray tubes. MethodsTo achieve this, data collected from ten machines in many regions of Cameroon were used (for nine machines) to build an initial model that does not take into account the anode angle and the tenth machine was used to test the model. Using the SpekCalc software, some simulations were carried out to evaluate the influence of the anode angle. This allowed the NMME to be proposed. ResultsThe deviations frequencies between 0.65% and 19.61% were obtained by comparing the output values obtained using initial model with the measured values. The statistical hypothesis test showed that the estimated values using initial model and NMME are in agreement with those measured unlike the Kothan and Tungjai model. For the tenth machine, the percentage difference between estimated and measured values is less than 8 %. ConclusionThese results show that the proposed model performed better than the previous models. In the absence of a dosimeter, the NMME could be used to estimate the output of high frequency X-ray machines and therefore the radiation doses received by patients during diagnostic X-ray examinations.

Dynamic interactions of HSV-2 and HIV/AIDS: A mathematical modeling approach

To enhance my research, I would like to share my knowledge of Herpes simplex virus-2 (HSV-2) and HIV/AIDS (Acquired Immunodeficiency Syndrome) through a mathematical model. The study’s objective is to develop and examine the co-disease model for the modern era using mathematical modeling. Based on their modes of transmission, HSV-2 and HIV/AIDS are currently the leading causes of death from infectious and severe chronic diseases. Depending on the severity of HIV-2’s chronic disease, the model is divided into five phases: the first two HIV-2 stages and the remaining three HIV stages. Ordinary differential equations (ODEs) are arranged differently by each individual. Investigations into the mathematical equation model have revealed the points of equilibrium between the free and endemic models. A study of the developed model was conducted using the basic reproduction numbers [R0] of HSV-2 and HIV. The results demonstrate that if R0<1, the free equilibrium of disease is asymptotically locally stable. When R0>1, equilibrium endemic states are regarded as existing. Finally, MATLAB software was used to simulate the numerical equations of the model.

Experimental and numerical analysis of the forced draft wet cooling tower

Cooling towers are essentially large boxes designed to maximize the evaporation of water. The inlet water temperature and water to air mass flow rate ratio (L/G) significantly affect the performance of the cooling tower. The number of a transfer unit (NTU), Merkel number (Me), Lewis number (Le), and efficiency of the cooling tower define the performance of the forced cooling tower. In this research paper, different inlet water temperatures ranging from 28 °C to 42 °C and (L/G) ranging from 0.5, 1, and 1.5 were used to investigate the performance of the forced cooling tower. Mathematical modeling equations were used to calculate NTU, Me, Le, and efficiency at different inlet water temperatures and (L/G). Engineering equation solver (EES) software was used to solve these mathematical modeling equations. Further, an experimental investigation was carried to find forced cooling tower performance at different inlet water temperatures and (L/G), and results were compared with the theoretical results. The results revealed that increasing the inlet water temperature, NTU, Me, Le, and efficiency increased and were directly related to each other. Further, NTU and efficiency were increased by increasing (L/G). At the same time, the Me and Le reduced with (L/G). Finally, an acceptable and better agreement has been obtained between experimental and theoretical results. Based on obtained results, it has been concluded that higher values of inlet water temperature and (L/G) provided the higher performance of the forced cooling tower.

Accurate prediction of Kp,uu,brain based on experimental measurement of Kp,brain and computed physicochemical properties of candidate compounds in CNS drug discovery

A mathematical equation model was developed by building the relationship between the fu,b/fu,p ratio and the computed physicochemical properties of candidate compounds, thereby predicting Kp,uu,brain based on a single experimentally measured Kp,brain value. A total of 256 compounds and 36 marketed published drugs including acidic, basic, neutral, zwitterionic, CNS-penetrant, and non-CNS penetrant compounds with diverse structures and physicochemical properties were involved in this study. A strong correlation was demonstrated between the fu,b/fu,p ratio and physicochemical parameters (CLogP and ionized fraction). The model showed good performance in both internal and external validations. The percentages of compounds with Kp,uu,brain predictions within 2-fold variability were 80.0 %–83.3 %, and more than 90 % were within a 3-fold variability. Meanwhile, “black box” QSAR models constructed by machine learning approaches for predicting fu,b/fu,p ratio based on the chemical descriptors are also presented, and the ANN model displayed the highest accuracy with an RMSE value of 0.27 and 86.7 % of the test set drugs fell within a 2-fold window of linear regression. These models demonstrated strong predictive power and could be helpful tools for evaluating the Kp,uu,brain by a single measurement parameter of Kp,brain during lead optimization for CNS penetration evaluation and ranking CNS drug candidate molecules in the early stages of CNS drug discovery.

Microstructure and properties of CoCrFeNiAlxMo2-x high-entropy alloy coating by laser cladding

CoCrFeNiAlxMo2-x (x = 0, 0.5, 1, 1.5, and 2) high-entropy alloy coatings were applied to Q235 steel, and this study investigated the effect of x variations on microstructure evolution and properties. It was fount that as x increased, the crystal structure of the coatings transitioned from a face-centred cubic (FCC) + body-centred cubic (BCC) + σ + B2 phase to a BCC + σ + B2 phase, and eventually it become a BCC phase. Concurrently, the microhardness, wear resistance, corrosion resistance, and high-temperature oxidation resistance of the coatings initially increased and then decreased with the rise in x. The optimal values were achieved at x = 1. The enhancement in microhardness and wear resistance of high-entropy alloy (HEA) coatings was attributed to the change of phase type, dispersion strengthening and solid solution strengthening. Adding of the Al element generated a passivation film on the coatings’ surface, which mitigated galvanic corrosion. Furthermore, an appropriate amount of Mo increased the thickness and density of the passivation film, thereby improving its corrosion resistance. During early-stage high-temperature oxidation, the Al underwent element undergoes rapid oxidation, while Mo promoted the formation of Al2O3, leading to an excellent high-temperature oxidation resistance. Additionally, mathematical model equations were used to fit the results, adding insights into the effects of Al and Mo content changes (x value) on the wear resistance, corrosion resistance, and high-temperature oxidation resistance of the coatings.

Simulation of blood flow in a stenosed and bifurcating artery using Finite Volume Methods and OpenFOAM

The article focuses on the shear-thinning and viscoelastic constitutive modelling and numerical simulation of blood flow in a stenosed and bifurcating artery. Specifically, the shear-thinning and viscoelastic behaviour of blood are modelled and implemented via the Oldroyd-B and Generalized Oldroyd-B constitutive models. A robust and efficient general purpose numerical (and computational) methodology for the simulation of blood flow in a stenosed and bifurcating artery is also developed and implemented. The numerical algorithm is developed more generally to resolve the mathematical model equations arising out of the all-encompassing Generalized Giesekus constitutive model. This model reduces to the Generalized Oldroyd-B model and subsequently also to the standard Oldroyd-B model simply by switching off certain material parameters. The inclusion of the Generalized Giesekus model must therefore be viewed in this context, to facilitate the development of an all encompassing general purpose numerical code. The blood flow modelling is otherwise done via the Oldroyd-B and Generalized Oldroyd-B constitutive models. The shear-thinning effects are implemented via the Cross model for shear-viscosity. The Generalized Oldroyd-B model results all illustrate that the velocity is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher would the velocity spurt through the constriction. This velocity behaviour correspondingly enhances the wall shear-stresses as the constriction increases, caused by the presence of the stenosis. High wall shear-stresses greatly increase the possibility of rupture of the stenosis. This can lead to catastrophic consequences in the usual case where the stenosis is caused, say, by tumor growth. As demonstrated near the contraction of a standard 4:1 contraction flow geometry, dramatic fluid flow effects, which are attributable to the polymeric-stresses, specifically to the first normal stress difference, are observed in the vicinity of the constrictions resulting from the presence of the stenosis. Such effects, include, flow recirculation and reversal, vortex formation, and spurt phenomena.

Effect of surface radiation on double diffusion convection in a low Mach number compressible gaseous mixture (H2–air)

This study aims to numerically investigate the effect of surface radiation on double diffusion convection in a low Mach number compressible gaseous mixture, specifically focusing on the H2–air system in a square cavity. The cavity is subjected to low horizontal temperature and concentration gradients and isolated from its flat walls. The mathematical model's equations were discretized using the finite volume method based on the semi-implicit method for pressure-linked equations revised algorithm for the pressure–velocity coupling. The radiosity method is employed to calculate the radiative heat exchange between the internal walls of the cavity. This work addresses a significant research gap by exploring the interplay between surface radiation, compressibility effects, and double diffusion convection. It makes a novel contribution to the field and has implications for combustion, astrophysics, and industrial heat exchange processes. Comparing the results with those obtained for a light gaseous mixture, the findings demonstrate that the presence of radiation considerably modifies the thermal, dynamic, and mass fields, as well as the thermophysical properties of the gaseous mixture in the case of heavy gaseous mixtures. These modifications can reach up to 20%.The outcomes of this study provide a foundation for further research and experimentation, with applications ranging from engineering to astrophysics.

TRANSPORTATION OF CUTTINGS BY DRILLING MUD IN HORIZONTAL WELLS. PART 1. MODELING THE STRUCTURE OF DISPERSED CURRENTS

Link for citation: Kharlamov S.N., Mehran Janghorbani, Zaykovskiy V.V. Transportation of cuttings by drilling mud in horizontal wells. Part 1. Modeling the structure of dispersed currents. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 10, рр. 34-48. In Rus. The relevance of the research is associated with the development of technical solutions for drilling wells with horizontal endings, in which cleaning the annulus from particles of drilled cuttings in hydraulic transport conditions seems technologically and economically efficient compared to other, for example, mechanical methods. The purpose of the article is to develop a computational methodology/approach to a detailed forecast and deep understanding of the physical mechanism of the influence of hydraulic transport on the well cleaning intensity. Moreover, the strategy of such a study is focused on the choice of flow conditions/rheological parameters of the model, in which the obtained detailed theoretical information on the evolution of the dynamic flow structure should be used in the development of design methods and the formulation of recommendations to engineering personnel for emergency warnings. The object of this study is a new class of viscous currents of dispersed media induced by external and internal forces, characteristic of the functioning of special equipment that ensures the movement of drilling mud with complex rheology in the well through an eccentric annular annulus. Results. The given article is the first part of the study devoted to solving complex problems accompanying the hydraulic transfer of rheologically complex mixtures through wells with an extended horizontal section and their cleaning from drilling cuttings. The first part presents the data on reasonable modeling of hydrodynamics of viscous dispersed mixture within the framework of reference to full equations describing laws of mass conservation, impulse for detection of peculiarities, determination of flow regularities in eccentric area of annular annulus, as well as search for ways of intensification of cleaning under conditions of real drilling. It is assumed that the viscous-inertial-gravitational flow of a liquid of the Herschel–Bulkly type with solid particles (sand) is carried out in conditions of laminar-turbulent, straight-flow and twisted (by the method of a movable wall) flow developing in the space. It is noted that the formation of modes with active and conservative action of external and internal forces allows efficient cleaning of the annulus. System of defining equations of mathematical model of hydrodynamics and mass transfer is analyzed for possibility of taking into account changes in nonlinearity of thermophysical properties, resistance to disturbances at boundaries of flow area and phase separation. It is noted that the prediction of molar processes is carried out within the framework of modern statistical models of the RANS method and the Euler–Lagrangian approach to describing the movement of heterogeneous media implemented in the ANSYS CFD software. It was shown that at the real drilling conditions, the mathematical model is successful in determining the spectrum of local and integral parameters of hydrodynamics and mass transfer in a wide range of changes in drilling conditions, which make it possible to understand the effects of particle sedimentation on the lower wall, the dynamics of vortex separation and the transfer of particles to the low-Reynolds region with a suspended state of the mixture structure and the inertial zone of the flow core. It is noted that the intensity of hydraulic transport downstream is significantly influenced by the conditions of phase entry, rheological characteristics of the mud. The calculations established the flow areas with satisfactory agreement of dynamic characteristics of the flow according to the proposed model with available experimental data, for example, shear stress at the wall, radial distributions of the components of the fluid velocity vector along the length of the well at different angles of deviation of its borehole from the vertical. Moreover, the results of this article should be taken into account when describing the data of the second part, as an addition to the study of hydraulic transport according to the proposed technique of real drilling of horizontal wells with optimal rheological properties of the mud.

Numerical Simulation of Chemical Propulsion Systems: Survey and Fundamental Mathematical Modeling Approach

This study deals with the mathematical modeling and numerical simulation of chemical propulsion systems (CPSs). For this, we investigate and summarize a comprehensive collection of the simulation modeling developments of CPSs in academic works, applications, and industrial fields. Then, we organize and analyze the simulation modeling approaches in several ways. After that, we organize differential-algebraic Equations (DAEs) for fundamental mathematical modeling consisting of the governing Equations (ordinary differential equations, ODEs) for the components and other equations derived from several physical rules or characteristics (algebraic equations or phenomenological equations, AEs) and then synthesize and summarize the fundamental structures of analytic mathematical modeling by types (liquid-propellant rocket engines, solid-propellant rocket motors, and hybrid-propellant rocket motors) of CPSs.