Search results for: polynomial constitutive equation

Authors: Seydou Sinde

Abstract:

The aims of this paper are to formulate mathematical expressions that can be used to estimate the standpipe pressure (SPP). The developed formulas take into account the main factors that, directly or indirectly, affect the behavior of SPP values. Fluid rheology and well hydraulics are some of these essential factors. Mud Plastic viscosity, yield point, flow power, consistency index, flow rate, drillstring, and annular geometries are represented by the frictional pressure (Pf), which is one of the input independent parameters and is calculated, in this paper, using Herschel-Bulkley rheological model. Other input independent parameters include the rate of penetration (ROP), applied load or weight on the bit (WOB), bit revolutions per minute (RPM), bit torque (TRQ), and hole inclination and direction coupled in the hole curvature or dogleg (DL). The technique of repeating parameters and Buckingham PI theorem are used to reduce the number of the input independent parameters into the dimensionless revolutions per minute (RPMd), the dimensionless torque (TRQd), and the dogleg, which is already in the dimensionless form of radians. Multivariable linear and polynomial regression technique using PTC Mathcad Prime 4.0 is used to analyze and determine the exact relationships between the dependent parameter, which is SPP, and the remaining three dimensionless groups. Three models proved sufficiently satisfactory to estimate the standpipe pressure: multivariable linear regression model 1 containing three regression coefficients for vertical wells; multivariable linear regression model 2 containing four regression coefficients for deviated wells; and multivariable polynomial quadratic regression model containing six regression coefficients for both vertical and deviated wells. Although that the linear regression model 2 (with four coefficients) is relatively more complex and contains an additional term over the linear regression model 1 (with three coefficients), the former did not really add significant improvements to the later except for some minor values. Thus, the effect of the hole curvature or dogleg is insignificant and can be omitted from the input independent parameters without significant losses of accuracy. The polynomial quadratic regression model is considered the most accurate model due to its relatively higher accuracy for most of the cases. Data of nine wells from the Middle East were used to run the developed models with satisfactory results provided by all of them, even if the multivariable polynomial quadratic regression model gave the best and most accurate results. Development of these models is useful not only to monitor and predict, with accuracy, the values of SPP but also to early control and check for the integrity of the well hydraulics as well as to take the corrective actions should any unexpected problems appear, such as pipe washouts, jet plugging, excessive mud losses, fluid gains, kicks, etc.

Keywords: standpipe, pressure, hydraulics, nondimensionalization, parameters, regression

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Authors: BenedictI Ita, Etido P. Inyang

Abstract:

In this work, the resolutions of the N-dimensional Schrödinger equation with the screened modified Kratzerplus inversely quadratic Yukawa potential (SMKIQYP) have been obtained with the Greene-Aldrich approximation scheme using the Nikiforov-Uvarov method. The eigenvalues and the normalized eigenfunctions are obtained. We then apply the energy spectrum to study four (HCl, N₂, NO, and CO) diatomic molecules. The results show that the energy spectra of these diatomic molecules increase as quantum numbers increase. The energy equation was also used to calculate the partition function and other thermodynamic properties. We predicted the partition function of CO and NO. To check the accuracy of our work, the special case (Modified Kratzer and screened Modified Kratzer potentials) of the collective potential energy eigenvalues agrees excellently with the existing literature.

Keywords: Schrödinger equation, Nikiforov-Uvarov method, modified screened Kratzer, inversely quadratic Yukawa potential, diatomic molecules

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Authors: Joseph Amponsah

Abstract:

This research proposes an equation to predict and determine the momentum source equation term after factoring in the radial friction between the fluid and the blades and the impeller's propulsive power. This research aims to look at how CFD software can be used to predict the effect of flows in nuclear reactor stirred tanks through a momentum source equation and the concentration distribution of tracers that have been introduced in reactor tanks. The estimated findings, including the dimensionless concentration curves, power, and pumping numbers, dimensionless velocity profiles, and mixing times 4, were contrasted with results from tests in stirred containers. The investigation was carried out in Part I for vessels that were agitated by one impeller on a central shaft. The two types of impellers employed were an ordinary Rushton turbine and a 6-bladed 45° pitched blade turbine. The simulations made use of numerous reference frame techniques and the common k-e turbulence model. The impact of the grid type was also examined; unstructured, structured, and unique user-defined grids were looked at. The CFD model was used to simulate the flow field within the Rushton turbine nuclear reactor stirred tank. This method was validated using experimental data that were available close to the impeller tip and in the bulk area. Additionally, analyses of the computational efficiency and time using MRF and SM were done.

Keywords: Ansys fluent, momentum equation, CFD, prediction

Procedia PDF Downloads 79

Authors: Ismail Seçer

Abstract:

The purpose of this study is to analyze the predictive effect of anxiety sensitivity on obsessive compulsive symptoms. The sample of the study consists of 542 students selected with appropriate sampling method from the secondary and high schools in Erzurum city center. Obsessive Compulsive Inventory and Anxiety Sensitivity Index were used in the study to collect data. The data obtained through the study was analyzed with structural equation modeling. As a result of the study, it was determined that there is a significant relationship between obsessive Compulsive Disorder (OCD) and anxiety sensitivity. Anxiety sensitivity has direct and indirect meaningful effects on the latent variable of OCD in the sub-dimensions of doubting-checking, obsessing, hoarding, washing, ordering, and mental neutralizing, and also anxiety sensitivity is a significant predictor of obsessive compulsive symptoms.

Keywords: obsession, compulsion, structural equation, anxiety sensitivity

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Authors: Ramon Santana

Abstract:

The use of biometric identifiers in the field of information security, access control to resources, authentication in ATMs and banking among others, are of great concern because of the safety of biometric data. In the general architecture of a biometric system have been detected eight vulnerabilities, six of them allow obtaining minutiae template in plain text. The main consequence of obtaining minutia templates is the loss of biometric identifier for life. To mitigate these vulnerabilities several models to protect minutiae templates have been proposed. Several vulnerabilities in the cryptographic security of these models allow to obtain biometric data in plain text. In order to increase the cryptographic security and ease of reversibility, a minutiae templates protection model is proposed. The model aims to make the cryptographic protection and facilitate the reversibility of data using two levels of security. The first level of security is the data transformation level. In this level generates invariant data to rotation and translation, further transformation is irreversible. The second level of security is the evaluation level, where the encryption key is generated and data is evaluated using a defined evaluation function. The model is aimed at mitigating known vulnerabilities of the proposed models, basing its security on the impossibility of the polynomial reconstruction.

Keywords: fingerprint, template protection, bio-cryptography, minutiae protection

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Authors: Merouane Salhi, Toufik Zebbiche

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When the stagnation pressure of perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas doesn’t remain perfect. Its state equation change and it becomes for a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation. The aim of this work is to show and discuss the effect of stagnation pressure on supersonic thermodynamical, physical and geometrical flow parameters, to find a general case for real gas. With the assumptions that Berthelot’s state equation accounts for the molecular size and intermolecular force effects, expressions are developed for analyzing supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The designs parameters for supersonic nozzle like thrust coefficient depend directly on stagnation parameters of the combustion chamber. The application is for air. A computation of error is made in this case to give a limit of perfect gas model compared to real gas model.

Keywords: supersonic flow, real gas model, Berthelot’s state equation, Simpson’s method, condensation function, stagnation pressure

Procedia PDF Downloads 447

Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Dong Wook Lee, Seung Hyun Kim

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Geological structure formed by volcanic activities shows polymorphic characteristics due to repeated cooling and hardening of lava. The Jeju region is showing polymorphic characteristics in which clinker layers are irregularly distributed along with vesicular basalt due to volcanic activities. Accordingly, resident damages and environmental disputes occur frequently in the Jeju region due to blasting. The purpose of this study is to develop a blast vibration equation considering the polymorphic characteristics of basaltic ground in Jeju. The blast vibration equation consists of a functional formula of the blasting vibration constant K that changes according to ground characteristics, and attenuation index n. The case study results in Jeju showed that if there are clinker layers, attenuation index n showed a distribution of -1.11~-1.87, whereas if there are no clinker layers, n was -2.79. Moreover, if there are no clinker layers, the frequency of blast vibration showed a high frequency band from 30Hz to 100Hz, while in rocks with clinker layers it showed a low frequency band from 10Hz to 20Hz.

Keywords: blast vibration equation, basaltic ground, clinker layer, blasting vibration constant, attenuation index

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Authors: Krutika K. Sawant, Anil Solanki

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The present study deals with the preparation and optimization of ethyl cellulose-containing disopyramide phosphate loaded microspheres using solvent evaporation technique. A central composite design consisting of a two-level full factorial design superimposed on a star design was employed for optimizing the preparation microspheres. The drug:polymer ratio (X1) and speed of the stirrer (X2) were chosen as the independent variables. The cumulative release of the drug at a different time (2, 6, 10, 14, and 18 hr) was selected as the dependent variable. An optimum polynomial equation was generated for the prediction of the response variable at time 10 hr. Based on the results of multiple linear regression analysis and F statistics, it was concluded that sustained action can be obtained when X1 and X2 are kept at high levels. The X1X2 interaction was found to be statistically significant. The drug release pattern fitted the Higuchi model well. The data of a selected batch were subjected to an optimization study using Box-Behnken design, and an optimal formulation was fabricated. Good agreement was observed between the predicted and the observed dissolution profiles of the optimal formulation.

Keywords: disopyramide phosphate, ethyl cellulose, microspheres, controlled release, Box-Behnken design, factorial design

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Ayan Giri, Lukaranjan Phukan, Shantanu Karmakar

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Structure and tectonics play a vital role in ore genesis and deposition. The existence of a swelling structure below the current level of a mine leads to the discovery of ores below some permeant developments of the mine. The discovery and the extraction of the ore body are very critical to sustain the business requirement of the mine. The challenge was to extract the ore without hampering the global stability of the mine. In order to do so, different mining options were considered and analysed by numerical modelling in FLAC3d software. The constitutive model prepared for this simulation is the improved unified constitutive model, which can better and more accurately predict the stress-strain relationships in a continuum model. The IUCM employs the Hoek-Brown criterion to determine the instantaneous Mohr-Coulomb parameters cohesion (c) and friction (ɸ) at each level of confining stress. The extra swelled part can be dimensioned as north-south strike width 50m, east-west strike width 50m. On the north side, already a stope (P1) is excavated of the dimension of 25m NS width. The different options considered were (a) Open stoping of extraction of southern part (P0) of 50m to the full extent, (b) Extraction of the southern part of 25m, then filling of both the primaries and extraction of secondary (S0) 25m in between. (c) Extraction of the southern part (P0) completely, preceded by backfill and modify the design of the secondary (S0) for the overall stability of the permanent excavation above the stoping.

Keywords: extraction, IUCM, FLAC 3D, stoping, tectonics

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Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf

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Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.

Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks

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Authors: Abdelmalek Ouannou, Adil Brouri, Laila Kadi, Tarik

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Switched reluctance motor (SRM) has a major interest in a large domain as in electric vehicle driving because of its wide range of speed operation, high performances, low cost, and robustness to run under degraded conditions. The purpose of the paper is to develop a new analytical approach for modeling SRM parameters. Then, an identification scheme is proposed to obtain the SRM parameters. Since the SRM is featured by a highly nonlinear behavior, modeling these devices is difficult. Then, it is convenient to develop an accurate model describing the SRM. Furthermore, it is always operated in the magnetically saturated mode to maximize the energy transfer. Accordingly, it is shown that the SRM can be accurately described by a generalized polynomial Hammerstein model, i.e., the parallel connection of several Hammerstein models having polynomial nonlinearity. Presently an analytical identification method is developed using a chirp excitation signal. Afterward, the parameters of the obtained model have been determined using Finite Element Method analysis. Finally, in order to show the effectiveness of the proposed method, a comparison between the true and estimate models has been performed. The obtained results show that the output responses are very close.

Keywords: switched reluctance motor, swept-sine signal, generalized Hammerstein model, nonlinear system

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Authors: Ewedafe Simon Uzezi

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In this paper we presented a method based on Domain Decomposition (DD) for parallelization of 1-D Sugarcane Equation on parallel platform with parallel paradigms on Master-Slave platform using Message Passing Interface (MPI). The 1-D Sugarcane Equation was discretized using explicit method of discretization requiring evaluation nof temporal and spatial distribution of temperature. This platform gives better predictions of the effects of temperature distribution of the sugarcane problem. This work presented parallel overheads with overlapping communication and communication across parallel computers with numerical results across different block sizes with scalability. However, performance improvement strategies from the DD on various mesh sizes were compared experimentally and parallel results show speedup and efficiency for the parallel algorithms design.

Keywords: sugarcane, parallelization, explicit method, domain decomposition, MPI

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Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Reza Mollapourasl, Majid Haghi

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In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

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Authors: Shanujah Mathuranayagam, William Fuentes, Samanthika Liyanapathirana

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This paper introduces an enhanced version of the coupled hydro-mechanical hypoplastic model. The model is able to simulate volumetric collapse upon wetting and incorporates suction effects on stiffness and strength. Its mechanical constitutive equation links Bishop’s effective stress with strain and suction, featuring a normal consolidation line (NCL) with a compression index (λ) presenting a non-linear dependency with the degree of saturation. The Bulk modulus has been modified to ensure that under rapid volumetric collapse, the stress state remains at the NCL. The coupled model comprises eighteen parameters, with nine for the hydraulic component and nine for the mechanical component. Hydraulic parameters are calibrated with the use of water retention curves (IWRC) across varied soil densities, while mechanical parameters undergo calibration using isotropic and triaxial tests on both unsaturated and saturated samples. The model's performance is analyzed through the back-calculation of two experimental studies: (i) wetting under different vertical stresses for Lower Cromer Till and (ii) isotropic loading and triaxial loading for undisturbed loess. The results confirm that the proposed model is able to predict the hydro-mechanical behavior of unsaturated soils.

Keywords: hypoplastic model, volumetric collapse, normal consolidation line, compression index (λ), degree of saturation, soil suction

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Aleksandar Dedic, Dusko Salemovic, Milorad Danilovic, Radomir Kuzmanovic

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This paper takes into consideration the influence of bonding energy of water on energy demand of vacuum wood drying using the specific method of obtaining sorption isotherms. The experiment was carried out on oak wood at vacuum pressures of: 0.7 bar, 0.5bar and 0.3bar. The experimental work was done to determine a mathematical equation between the moisture content and energy of water-bonding. This equation helps in finding the average amount of energy of water-bonding necessary in calculation of energy consumption by use of the equation of heat balance in real drying chambers. It is concluded that the energy of water-bonding is large enough to be included into consideration. This energy increases at lower values of moisture content, when drying process approaches to the end, and its average values are lower on lower pressure.

Keywords: bonding energy, drying, isosters, oak, vacuum

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Authors: Suprit Pradhan, Sushil Pradhan

Abstract:

Photosynthesis is a physiological process where green plants prepare their food from carbon dioxide from the atmosphere and water being absorbed from the soil in presence of sun light and chlorophyll. From this definition it is clear that four reactants (Carbon Dioxide, Water, Light and Chlorophyll) are essential for the process to proceed and the product is a sugar or carbohydrate ultimately stored as starch. The entire process has “Light Reaction” (Photochemical) and “Dark Reaction” (Biochemical). Biochemical reactions are very much complicated being catalysed by various enzymes and the path of carbon is known as “Calvin Cycle” according to the name of its discover. The overall reaction which is now universally accepted can be explained like this. Six molecules of carbon dioxide react with twelve molecules of water in presence of chlorophyll and sun light to give only one molecule of sugar (Carbohydrate) six molecules of water and six molecules of oxygen is being evolved in gaseous form. This is the accepted equation and also chemically balanced. However while teaching the subject the author came across a new balanced equation from among the students who happened to be the daughter of the author. In the new balanced equation in place of twelve water molecules in the reactant side seven molecules can be expressed and accordingly in place of six molecules of water in the product side only one molecule of water is produced. The energetics of the photosynthesis as related to the environment and the newly reported balanced chemical equation has been discussed in detail in the present research paper presentation in this international conference on energy, environmental and chemical engineering.

Keywords: biochemistry, enzyme , isotope, photosynthesis

Procedia PDF Downloads 511

Authors: Piyarat Parklug, Busaba Supawattanaobodee, Penpat Pinyowattanasilp

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The radioactive iodine thyroid uptake (RAIU) has been widely used to differentiate the cause of thyrotoxicosis and treatment. Twenty-four hours RAIU is routinely used to calculate the dose of radioactive iodine (RAI) therapy; however, 2 days protocol is required. This study aims to evaluate the modification of Penpat Pinyowattanasilp equation application by the exclusion of outlier data, 3 hours RAIU less than 20% and more than 80%, to improve prediction of 24-hour uptake. The equation is predicted 24 hours RAIU (P24RAIU) = 32.5+0.702 (3 hours RAIU). Then calculating separation first and second therapeutic doses in Graves’ disease patients. Methods; This study was a retrospective study at Faculty of Medicine Vajira Hospital in Bangkok, Thailand. Inclusion were Graves’ disease patients who visited RAI clinic between January 2014-March 2019. We divided subjects into 2 groups according to first and second therapeutic doses. Results; Our study had a total of 151 patients. The study was done in 115 patients with first RAI dose and 36 patients with second RAI dose. The P24RAIU are highly correlated with actual 24-hour RAIU in first and second therapeutic doses (r = 0.913, 95% CI = 0.876 to 0.939 and r = 0.806, 95% CI = 0.649 to 0.897). Bland-Altman plot shows that mean differences between predictive and actual 24 hours RAI in the first dose and second dose were 2.14% (95%CI 0.83-3.46) and 1.37% (95%CI -1.41-4.14). The mean first actual and predictive therapeutic doses are 8.33 ± 4.93 and 7.38 ± 3.43 milliCuries (mCi) respectively. The mean second actual and predictive therapeutic doses are 6.51 ± 3.96 and 6.01 ± 3.11 mCi respectively. The predictive therapeutic doses are highly correlated with the actual dose in first and second therapeutic doses (r = 0.907, 95% CI = 0.868 to 0.935 and r = 0.953, 95% CI = 0.909 to 0.976). Bland-Altman plot shows that mean difference between predictive and actual P24RAIU in the first dose and second dose were less than 1 mCi (-0.94 and -0.5 mCi). This modification equation application is simply used in clinical practice especially patient with 3 hours RAIU in range of 20-80% in a Thai population. Before use, this equation for other population should be tested for the correlation.

Keywords: equation, Graves’disease, prediction, 24-hour uptake

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Authors: Samuel Ahamefula Mba

Abstract:

Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

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Authors: Ismail Seçer

Abstract:

The purpose of this study is to analyze the relationship between school burnout and academic motivation in high school students. The working group of the study consists of 455 students from the high schools in Erzurum city center, selected with appropriate sampling method. School Burnout Scale and Academic Motivation Scale were used in the study to collect data. Correlation analysis and structural equation modeling were used in the analysis of the data collected through the study. As a result of the study, it was determined that there are significant and negative relations between school burnout and academic motivation, and the school burnout has direct and indirect significant effects on the getting over himself, using knowledge and exploration dimension through the latent variable of academic motivation. Lastly, it was determined that school burnout is a significant predictor of academic motivation.

Keywords: school burnout, motivation, structural equation modeling, university

Procedia PDF Downloads 324

Authors: Aliakbar Golshani, Seyyed Mehdi Poorhashemi, Mahsa Gharizadeh

Abstract:

The under passing tunnels are strongly influenced by the soils around. There are some complexities in the specification of real soil behavior, owing to the fact that lots of uncertainties exist in soil properties, and additionally, inappropriate soil constitutive models. Such mentioned factors may cause incompatible settlements in numerical analysis with the obtained values in actual construction. This paper aims to report a case study on a specific tunnel constructed by NATM. The tunnel has a depth of 11.4 m, height of 12.2 m, and width of 14.4 m with 2.5 lanes. The numerical modeling was based on a 2D finite element program. The soil material behavior was modeled by hardening soil model. According to the field observations, the numerical estimated settlement at the ground surface was approximately four times more than the measured one, after the entire installation of the initial lining, indicating that some unknown factors affect the values. Consequently, the geotechnical parameters are accurately revised by a numerical back-analysis using laboratory and field test data and based on the obtained monitoring data. The obtained result confirms that typically, the soil parameters are conservatively low-estimated. And additionally, the constitutive models cannot be applied properly for all soil conditions.

Keywords: NATM tunnel, initial lining, laboratory test data, numerical back-analysis

Procedia PDF Downloads 361

Authors: Merouane Salhi, Toufik Zebbiche, Omar Abada

Abstract:

When the stagnation pressure of perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas does not remain perfect. Its state equation change and it becomes a real gas. In this case, the effects of molecular size and inter molecular attraction forces intervene to correct the state equation. The aim of this work is to show and discuss the effect of stagnation pressure on supersonic thermo dynamical, physical and geometrical flow parameters, to find a general case for real gas. With the assumptions that Berthelot’s state equation accounts for molecular size and inter molecular force effects, expressions are developed for analyzing supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The designs parameters for supersonic nozzle like thrust coefficient depend directly on stagnation parameters of the combustion chamber. The application is for air. A computation of error is made in this case to give a limit of perfect gas model compared to real gas model.

Keywords: supersonic flow, real gas model, Berthelot’s state equation, Simpson’s method, condensation function, stagnation pressure

Procedia PDF Downloads 524

Authors: Abbas Ebrahimi, Mohammad Zandsalimy

Abstract:

The main purpose of this study is to investigate the feasibility of using FPGA (Field Programmable Gate Arrays) chips as alternatives for the conventional CPUs to accelerate the numerical solution of the Laplace equation. FPGA is an integrated circuit that contains an array of logic blocks, and its architecture can be reprogrammed and reconfigured after manufacturing. Complex circuits for various applications can be designed and implemented using FPGA hardware. The reconfigurable hardware used in this paper is an SoC (System on a Chip) FPGA type that integrates both microprocessor and FPGA architectures into a single device. In the present study the Laplace equation is implemented and solved numerically on both reconfigurable hardware and CPU. The precision of results and speedups of the calculations are compared together. The computational process on FPGA, is up to 20 times faster than a conventional CPU, with the same data precision. An analytical solution is used to validate the results.

Keywords: accelerating numerical solutions, CFD, FPGA, hardware definition language, numerical solutions, reconfigurable hardware

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Authors: Darsh N. Patel, Eric Olson

Abstract:

Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: Mohammad Reza Shahnazari, Reza Kazemi, Ali Saberi

Abstract:

Most of the engineering problems are in nonlinear forms. Nonlinear boundary layer problems defined in infinite intervals contain specific complexities, especially in boundary layer condition conformance. As an example of these nonlinear complex problems, the well-known Blasius equation can be mentioned, which itself is one of the classic boundary layer problems. No analytical solution has been proposed yet for the Blasius equation due to its complexity. In this paper, an analytical method, namely the Kourosh method, based on the singularity perturbation method and the Liao homotopy analysis is utilized to solve the Blasius problem. In this method, an inner solution is developed in the [0,1] interval to expedite the solution convergence. The magnitude of the f ˝(0), as an essential quantity for determining the physical parameters, is directly calculated from the solution of the boundary condition problem. The advantages of this solution are that it does not need any numerical solution, it has a closed form and that its validation is shown in the entire [0,∞] interval. Furthermore, all of the desirable parameters could be extracted through a series of simple analytical operations from the final solution. This solution also satisfies the continuity conditions, which is one of the main contributions of this paper in comparison with most of the other proposed analytical solutions available in the literature. Comparison with numerical solutions reveals that the proposed method is highly accurate and convenient for application.

Keywords: Blasius equation, boundary layer, Kourosh method, analytical solution

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Authors: James Killian, Sarah Cox

Abstract:

The use of stability criteria within geotechnical engineering is the way the results of analyses are conveyed, and sensitivities and risk assessments are performed. Historically, the primary stability criteria for slope design has been the Factor of Safety (FOS) coming from a limit calculation. Increasingly, the value derived from Strength Reduction Factor (SRF) analysis is being used as the criteria for stability analysis. The purpose of this work was to study in detail the relationship between SRF values produced from a numerical modeling technique and the traditional FOS values produced from Limit Equilibrium (LEM) analyses. This study utilized a model of a 3000-foot-high slope with a 45-degree slope angle, assuming a perfectly plastic mohr-coulomb constitutive model with high cohesion and friction angle values typical of a large hard rock mine slope. A number of variables affecting the values of the SRF in a numerical analysis were tested, including zone size, in-situ stress, tensile strength, and dilation angle. This paper demonstrates that in most cases, SRF values are lower than the corresponding LEM FOS values. Modeled zone size has the greatest effect on the estimated SRF value, which can vary as much as 15% to the downside compared to FOS. For consistency when using SRF as a stability criteria, the authors suggest that numerical model zone sizes should not be constructed to be smaller than about 1% of the overall problem slope height and shouldn’t be greater than 2%. Future work could include investigations of the effect of anisotropic strength assumptions or advanced constitutive models.

Keywords: FOS, SRF, LEM, comparison

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