Search results for: elliptic equations

Authors: Najibullah M, Soumendra Nath Kuiry

Abstract:

Dams and reservoirs are perceived for their estimable alms to irrigation, water supply, flood control, electricity generation, etc. which civilize the prosperity and wealth of society across the world. Meantime the dam breach could cause devastating flood that can threat to the human lives and properties. Failures of large dams remain fortunately very seldom events. Nevertheless, a number of occurrences have been recorded in the world, corresponding in an average to one to two failures worldwide every year. Some of those accidents have caused catastrophic consequences. So it is decisive to predict the dam break flow for emergency planning and preparedness, as it poses high risk to life and property. To mitigate the adverse impact of dam break, modeling is necessary to gain a good understanding of the temporal and spatial evolution of the dam-break floods. This study will mainly deal with one-dimensional (1D) dam break modeling. Less commonly used in the hydraulic research community, another possible option for modeling the rapidly varied dam-break flows is the extended Boussinesq equations (BEs), which can describe the dynamics of short waves with a reasonable accuracy. Unlike the Shallow Water Equations (SWEs), the BEs taken into account the wave dispersion and non-hydrostatic pressure distribution. To capture the dam-break oscillations accurately it is very much needed of at least fourth-order accurate numerical scheme to discretize the third-order dispersion terms present in the extended BEs. The scope of this work is therefore to develop an 1D fourth-order accurate in both space and time Boussinesq model for dam-break flow analysis by using finite-volume / finite difference scheme. The spatial discretization of the flux and dispersion terms achieved through a combination of finite-volume and finite difference approximations. The flux term, was solved using a finite-volume discretization whereas the bed source and dispersion term, were discretized using centered finite-difference scheme. Time integration achieved in two stages, namely the third-order Adams Basforth predictor stage and the fourth-order Adams Moulton corrector stage. Implementation of the 1D Boussinesq model done using PYTHON 2.7.5. Evaluation of the performance of the developed model predicted as compared with the volume of fluid (VOF) based commercial model ANSYS-CFX. The developed model is used to analyze the risk of cascading dam failures similar to the Panshet dam failure in 1961 that took place in Pune, India. Nevertheless, this model can be used to predict wave overtopping accurately compared to shallow water models for designing coastal protection structures.

Keywords: Boussinesq equation, Coastal protection, Dam-break flow, One-dimensional model

Procedia PDF Downloads 232

Authors: Z. Jovanovic, Z. Masonicic, S. Dragutinovic, Z. Sakota

Abstract:

In this paper, a methodology for noise reduction of motor vehicles in use is presented. The methodology relies on synergic model of noise generation as a function of time. The arbitrary number of motor vehicle noise sources act in concert yielding the generation of the overall noise level of motor vehicle thereafter. The number of noise sources participating in the overall noise level of motor vehicle is subjected to the constraint of the calculation of the acoustic potential of each noise source under consideration. It is the prerequisite condition for the calculation of the acoustic potential of the whole vehicle. The recast form of pertinent set of equations describing the synergic model is laid down and solved by dint of Gauss method. The bunch of results emerged and some of them i.e. those ensuing from model application to MDD FAP Priboj motor vehicle in use are particularly elucidated.

Keywords: noise abatement, MV noise sources, noise source identification, muffler

Procedia PDF Downloads 448

Authors: Labane Chrif

Abstract:

A nonlinear approach to the automatic pitch attitude control problem for aircraft transportation is presented. A nonlinear model describing the longitudinal equations of motion in strict feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free design parameters. The controller is evaluated using the aircraft transportation. The adaptation scheme proposed allowed us to design an explicit controller with a minimal knowledge of the aircraft aerodynamics. Finally, the simulation results will show that backstepping controller have better dynamic performance, simpler design, higher precision, easier implement, etc. At the same time, the control effect will be significantly improved. In addition, backstepping control is superior in short transition, good stability, anti-disturbance and good control.

Keywords: nonlinear control, backstepping, aircraft control, Lyapunov function, longitudinal model

Procedia PDF Downloads 581

Authors: Lokeswara Rao P., Naga Venkata Rakesh N., V. Anantha Subramanian

Abstract:

It is important to estimate, predict, and avoid the dynamic instability of high speed planing crafts. It is known that design parameters like relative location of center of gravity with respect to the dynamic lift centre and length to beam ratio of the craft have influence on the tendency to porpoise. This paper analyzes the hydrodynamic performance on the basis of the semi-empirical Savitsky method and also estimates the same by numerical simulations based on Reynolds Averaged Navier Stokes (RANS) equations using a commercial code namely, STAR- CCM+. The paper examines through the same numerical simulation considering dynamic equilibrium, the changing running trim, which results in porpoising. Some interesting results emerge from the study and this leads to early detection of the instability.

Keywords: CFD, planing hull, porpoising, Savitsky method

Procedia PDF Downloads 181

Authors: El Hansali Hasnaa, Bennani Mohammed

Abstract:

Hexapod legged robot’s missions, particularly in irregular and dangerous areas, require high stability and high precision. In this paper, we consider the rectangular architecture body of legged robots with six legs distributed symmetrically along two sides, each leg contains three degrees of freedom for greater mobility. The aim of this work is planning tripod gait trajectory, based on the computing of the kinematic model to determine the joint variables in the lifting and the propelling phases. For this, appropriate coordinate frames are attached to the body and legs in order to obtain clear representation and efficient generation of the system equations. A simulation in MATLAB software platform is developed to confirm the kinematic model and various trajectories to the tripod gait adopted by the hexapod robot in its locomotion.

Keywords: hexapod legged robot, inverse kinematic model, simulation in MATLAB, tripod gait

Procedia PDF Downloads 278

Authors: Delara Soltani, Sajad Alimohammadi, Tim Persoons

Abstract:

Microfluidic technology reveals a new area of research in drug delivery, biomedical diagnostics, and the food and chemical industries. Mixing is an essential part of microfluidic devices. There is a need for fast and homogeneous mixing in microfluidic devices. On the other hand, mixing is difficult to achieve in microfluidic devices because of the size and laminar flow in these devices. In this study, a hybrid passive micromixer of a curved channel with obstacles inside the channel is designed. The computational fluid dynamic method is employed to solve governing equations. The results show that using obstacles can improve mixing efficiency in spiral micromixers. the effects of Reynolds number, number, and position of baffles are investigated. In addition, the effect of baffles on pressure drop is presented. this novel micromixer has the potential to utilize in microfluidic devices.

Keywords: CFD, micromixer, microfluidics, spiral, reynolds number

Procedia PDF Downloads 91

Authors: Sebastian Andersen, Peter N. Poulsen

Abstract:

The use of basis projection in the structural dynamic analysis is frequently applied. The purpose of the method is to improve the computational efficiency, while maintaining a high solution accuracy, by projection the governing equations onto a small set of carefully selected basis vectors. The present work considers basis projection in kinematic nonlinear systems with a focus on two widely used basis vectors; the system mode shapes and their modal derivatives. Particularly the latter basis vectors are given special attention since only approximate modal derivatives have been used until now. In the present work the complete modal derivatives, derived from perturbation methods, are presented and compared to the previously applied approximate modal derivatives. The correctness of the complete modal derivatives is illustrated by use of an example of a harmonically loaded kinematic nonlinear structure modeled by beam elements.

Keywords: basis projection, finite element method, kinematic nonlinearities, modal derivatives

Procedia PDF Downloads 237

Authors: Farid Khosravikia, Patricia Clayton

Abstract:

The main objective of this work is to evaluate the advantages and disadvantages of various machine learning techniques in two key steps of seismic hazard and risk assessment of different types of structures. The first step is the development of ground-motion models, which are used for forecasting ground-motion intensity measures (IM) given source characteristics, source-to-site distance, and local site condition for future events. IMs such as peak ground acceleration and velocity (PGA and PGV, respectively) as well as 5% damped elastic pseudospectral accelerations at different periods (PSA), are indicators of the strength of shaking at the ground surface. Typically, linear regression-based models, with pre-defined equations and coefficients, are used in ground motion prediction. However, due to the restrictions of the linear regression methods, such models may not capture more complex nonlinear behaviors that exist in the data. Thus, this study comparatively investigates potential benefits from employing other machine learning techniques as statistical method in ground motion prediction such as Artificial Neural Network, Random Forest, and Support Vector Machine. The results indicate the algorithms satisfy some physically sound characteristics such as magnitude scaling distance dependency without requiring pre-defined equations or coefficients. Moreover, it is shown that, when sufficient data is available, all the alternative algorithms tend to provide more accurate estimates compared to the conventional linear regression-based method, and particularly, Random Forest outperforms the other algorithms. However, the conventional method is a better tool when limited data is available. Second, it is investigated how machine learning techniques could be beneficial for developing probabilistic seismic demand models (PSDMs), which provide the relationship between the structural demand responses (e.g., component deformations, accelerations, internal forces, etc.) and the ground motion IMs. In the risk framework, such models are used to develop fragility curves estimating exceeding probability of damage for pre-defined limit states, and therefore, control the reliability of the predictions in the risk assessment. In this study, machine learning algorithms like artificial neural network, random forest, and support vector machine are adopted and trained on the demand parameters to derive PSDMs for them. It is observed that such models can provide more accurate estimates of prediction in relatively shorter about of time compared to conventional methods. Moreover, they can be used for sensitivity analysis of fragility curves with respect to many modeling parameters without necessarily requiring more intense numerical response-history analysis.

Keywords: artificial neural network, machine learning, random forest, seismic risk analysis, seismic hazard analysis, support vector machine

Procedia PDF Downloads 106

Authors: Aliakbar Sayadi, Thomas R. Neitzert, G. Charles Clifton, Min Cheol Han

Abstract:

The present study aims to assess the performance of vermiculite concrete containing poly-lactic acid beads as an eco-friendly aggregate. Vermiculite aggregate was replaced by poly-lactic acid in percentages of 0%, 20%, 40%, 60% and 80%. Mechanical and thermal properties of concrete were investigated. Test results indicated that the inclusion of poly-lactic acid decreased the PH value of concrete and all the poly-lactic acid particles were dissolved due to the formation of sodium lactide and lactide oligomers when subjected to the high alkaline environment of concrete. In addition, an increase in thermal conductivity value of concrete was observed as the ratio of poly-lactic acid increased. Moreover, a set of equations was proposed to estimate the water-cement ratio, cement content and water absorption ratio of concrete.

Keywords: poly-lactic acid (PLA), vermiculite concrete, eco-friendly, mechanical properties

Procedia PDF Downloads 404

Authors: Khairil I. Othman, Nur N. Kamal, Zarina B. Ibrahim

Abstract:

In this paper, we present modified Newton method as a new strategy for improving the efficiency of Two Point Block Backward Differentiation Formulas (BBDF) when solving stiff systems of ordinary differential equations (ODEs). These methods are constructed to produce two approximate solutions simultaneously at each iteration The detailed implementation of the predictor corrector BBDF with PE(CE)2 with modified Newton are discussed. The proposed modification of BBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing Block Backward Differentiation Formula. Numerical results show the advantage of using the new strategy for solving stiff ODEs in improving the accuracy of the solution.

Keywords: newton method, two point, block, accuracy

Procedia PDF Downloads 357

Authors: Frederick Ferguson, Dehua Feng, Yang Gao

Abstract:

No doubt, current CFD tools have a great many technical limitations, and active research is being done to overcome these limitations. Current areas of limitations include vortex-dominated flows, separated flows, and turbulent flows. In general, turbulent flows are unsteady solutions to the fluid dynamic equations, and instances of these solutions can be computed directly from the equations. One of the approaches commonly implemented is known as the ‘direct numerical simulation’, DNS. This approach requires a spatial grid that is fine enough to capture the smallest length scale of the turbulent fluid motion. This approach is called the ‘Kolmogorov scale’ model. It is of interest to note that the Kolmogorov scale model must be captured throughout the domain of interest and at a correspondingly small-time step. In typical problems of industrial interest, the ratio of the length scale of the domain to the Kolmogorov length scale is so great that the required grid set becomes prohibitively large. As a result, the available computational resources are usually inadequate for DNS related tasks. At this time in its development, DNS is not applicable to industrial problems. In this research, an attempt is made to develop a numerical technique that is capable of delivering DNS quality solutions at the scale required by the industry. To date, this technique has delivered preliminary results for both steady and unsteady, viscous and inviscid, compressible and incompressible, and for both high and low Reynolds number flow fields that are very accurate. Herein, it is proposed that the Integro-Differential Scheme (IDS) be applied to a set of vortex-shockwave interaction problems with the goal of investigating the nonstationary physics within the resulting interaction regions. In the proposed paper, the IDS formulation and its numerical error capability will be described. Further, the IDS will be used to solve the inviscid and viscous Burgers equation, with the goal of analyzing their solutions over a considerable length of time, thus demonstrating the unsteady capabilities of the IDS. Finally, the IDS will be used to solve a set of fluid dynamic problems related to flow that involves highly vortex interactions. Plans are to solve the following problems: the travelling wave and vortex problems over considerable lengths of time, the normal shockwave–vortex interaction problem for low supersonic conditions and the reflected oblique shock–vortex interaction problem. The IDS solutions obtained in each of these solutions will be explored further in efforts to determine the distributed density gradients and vorticity, as well as the Q-criterion. Parametric studies will be conducted to determine the effects of the Mach number on the intensity of vortex-shockwave interactions.

Keywords: vortex dominated flows, shockwave interactions, high Reynolds number, integro-differential scheme

Procedia PDF Downloads 139

Authors: Mohamed Fawzy Elzarei, Yousef Mohammed Al-Dakheel, Ali Mohamed Alseaf

Abstract:

Modern molecular techniques, like single marker analysis for linked traits to these markers, can provide us with rapid and accurate genetic results. In the last two decades of the last century, the applications of molecular techniques were reached a faraway point in cattle, sheep, and pig. In goats, especially in our region, the application of molecular techniques is still far from other species. As reported by many researchers, microsatellites marker is one of the suitable markers for lie studies. The single marker linked to traits of interest is one technique allowed us to early select animals without the necessity for mapping the entire genome. Simplicity, applicability, and low cost of this technique gave this technique a wide range of applications in many areas of genetics and molecular biology. Also, this technique provides a useful approach for evaluating genetic differentiation, particularly in populations that are poorly known genetically. The expected breeding value (EBV) and yield deviation (YD) are considered as the most parameters used for studying the linkage between quantitative characteristics and molecular markers, since these values are raw data corrected for the non-genetic factors. A total of 17 microsatellites markers (from chromosomes 6, 14, 18, 20 and 23) were used in this study to search for areas that could be responsible for genetic variability for some milk traits and search of chromosomal regions that explain part of the phenotypic variance. Results of single-marker analyses were used to identify the linkage between microsatellite markers and variation in EBVs of these traits, Milk yield, Protein percentage, Fat percentage, Litter size and weight at birth, and litter size and weight at weaning. The estimates of the parameters from forward and backward solutions using stepwise regression procedure on milk yield trait, only two markers, OARCP9 and AGLA29, showed a highly significant effect (p≤0.01) in backward and forward solutions. The forward solution for different equations conducted that R2 of these equations were highly depending on only two partials regressions coefficient (βi,) for these markers. For the milk protein trait, four marker showed significant effect BMS2361, CSSM66 (p≤0.01), BMS2626, and OARCP9 (p≤0.05). By the other way, four markers (MCM147, BM1225, INRA006, andINRA133) showed highly significant effect (p≤0.01) in both backward and forward solutions in association with milk fat trait. For both litter size at birth and at weaning traits, only one marker (BM143(p≤0.01) and RJH1 (p≤0.05), respectively) showed a significant effect in backward and forward solutions. The estimates of the parameters from forward and backward solution using stepwise regression procedure on litter weight at birth (LWB) trait only one marker (MCM147) showed highly significant effect (p≤0.01) and two marker (ILSTS011, CSSM66) showed a significant effect (p≤0.05) in backward and forward solutions.

Keywords: microsatellites marker, estimated breeding value, stepwise regression, milk traits

Procedia PDF Downloads 93

Authors: Marcin Sowa

Abstract:

The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

Procedia PDF Downloads 206

Authors: Ioana Neamtu

Abstract:

This paper investigates the potential for demand-side management for the system price in the Nordic electricity market and the price effects of introducing wind-power into the system. The model proposed accounts for the micro-structure of the Nordic electricity market by modeling each hour individually, while still accounting for the relationship between the hours within a day. This flexibility allows us to explore the differences between peak and shoulder demand hours. Preliminary results show potential for demand response management, as indicated by the price elasticity of demand as well as a small but statistically significant decrease in price, given by the wind power penetration. Moreover, our study shows that these effects are stronger during day-time and peak hours,compared to night-time and shoulder hours.

Keywords: structural model, GMM estimation, system of equations, electricity market

Procedia PDF Downloads 437

Authors: Prem Singh, Jagdeep Singh

Abstract:

In an attempt to investigate the performance of single basin solar still for climate conditions of Ludhiana a single basin solar still was designed, fabricated and tested. The energy balance equations for various parts of the still are solved by Gauss-Seidel iteration method. Computer model was made and experimentally validated. The validated computer model was used to estimate the annual distillation yield and performance ratio of the still for Ludhiana. The Theoretical and experimental distillation yield were 4318.79 ml and 3850 ml, respectively for the typical day. The predicted distillation yield was 12.5% higher than the experimental yield. The annual distillation yield per square meter aperture area and annual performance ratio for single basin solar still is 1095 liters and 0.43 liters, respectively. The payback period for micro-stepped solar still is 2.5 years.

Keywords: solar distillation, solar still, single basin, still

Procedia PDF Downloads 505

Authors: Dahia Chibouti, Benoit Trouette, Eric Chenier

Abstract:

With the development of micro-electro-mechanical systems (MEMS), understanding fluid flow and heat transfer at the micrometer scale is crucial. In the case where the flow characteristic length scale is narrowed to around ten times the mean free path of gas molecules, the classical fluid mechanics and energy equations are still valid in the bulk flow, but particular attention must be paid to the gas/solid interface boundary conditions. Indeed, in the vicinity of the wall, on a thickness of about the mean free path of the molecules, called the Knudsen layer, the gas molecules are no longer in local thermodynamic equilibrium. Therefore, macroscopic models based on the continuity of velocity, temperature and heat flux jump conditions must be applied at the fluid/solid interface to take this non-equilibrium into account. Although these macroscopic models are widely used, the assumptions on which they depend are not necessarily verified in realistic cases. In order to get rid of these assumptions, simulations at the molecular scale are carried out to study how molecule interaction with walls can change the fluid flow and heat transfers at the vicinity of the walls. The developed approach is based on a kind of heterogeneous multi-scale method: micro-domains overlap the continuous domain, and coupling is carried out through exchanges of information between both the molecular and the continuum approaches. In practice, molecular dynamics describes the fluid flow and heat transfers in micro-domains while the Navier-Stokes and energy equations are used at larger scales. In this framework, two kinds of micro-simulation are performed: i) in bulk, to obtain the thermo-physical properties (viscosity, conductivity, ...) as well as the equation of state of the fluid, ii) close to the walls to identify the relationships between the slip velocity and the shear stress or between the temperature jump and the normal temperature gradient. The coupling strategy relies on an implicit formulation of the quantities extracted from micro-domains. Indeed, using the results of the molecular simulations, a Bayesian regression is performed in order to build continuous laws giving both the behavior of the physical properties, the equation of state and the slip relationships, as well as their uncertainties. These latter allow to set up a learning strategy to optimize the number of micro simulations. In the present contribution, the first results regarding this coupling associated with the learning strategy are illustrated through parametric studies of convergence criteria, choice of basis functions and noise of input data. Anisothermic flows of a Lennard Jones fluid in micro-channels are finally presented.

Keywords: multi-scale, microfluidics, micro-channel, hybrid approach, coupling

Procedia PDF Downloads 168

Authors: Abderazak Guettaf

Abstract:

The mathematical models of the physical phenomena interacting in inductive plasma were described by the physics equations of the continuous mediums. A 3D model based on magnetic potential vector and electric scalar potential (A, V) formulation is used. The finished volume method is applied to electromagnetic equation, to obtain the field distribution inside the plasma. The numerical results of the method developed on a basic model designed starting from a real three-dimensional model were exposed. From the mathematical model 3D spreading assumptions and boundary conditions, we evaluated the electric field in the load and we have developed a numerical code made under the MATLAB environment, all verifying the effectiveness and validity of this code.

Keywords: electric field, 3D magnetic potential vector and electric scalar potential (A, V) formulation, finished volumes, annular plasma

Procedia PDF Downloads 494

Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah

Abstract:

A new numerical algorithm is developed to solve coupled convection-radiation heat transfer in a two dimensional enclosure. Radiative heat transfer in participating medium has been carried out using the control volume finite element method (CVFEM). The radiative transfer equations (RTE) are formulated for absorbing, emitting and scattering medium. The density, velocity and temperature fields are calculated using the two double population lattice Boltzmann equation (LBE). In order to test the efficiency of the developed method the Rayleigh Benard convection with and without radiative heat transfer is analyzed. The obtained results are validated against available works in literature and the proposed method is found to be efficient, accurate and numerically stable.

Keywords: participating media, LBM, CVFEM- radiation coupled with convection

Procedia PDF Downloads 408

Authors: Naseem Uddin

Abstract:

Impinging jets are used in variety of engineering and industrial applications. This paper is based on numerical simulations of heat transfer by turbulent impinging jet with velocity field excitations using different Reynolds Averaged Navier-Stokes Equations models. Also Detached Eddy Simulations are conducted to investigate the differences in the prediction capabilities of these two simulation approaches. In this paper the excited jet is simulated in non-commercial CFD code OpenFOAM with the goal to understand the influence of dynamics of impinging jet on heat transfer. The jet’s frequencies are altered keeping in view the preferred mode of the jet. The Reynolds number based on mean velocity and diameter is 23,000 and jet’s outlet-to-target wall distance is 2. It is found that heat transfer at the target wall can be influenced by judicious selection of amplitude and frequencies.

Keywords: excitation, impinging jet, natural frequency, turbulence models

Procedia PDF Downloads 274

Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

Abstract:

The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

Procedia PDF Downloads 112

Authors: Chang Su Woo, Hyun Sung Park

Abstract:

Useful lifetime evaluation of chevron rubber spring was very important in design procedure to assure the safety and reliability. It is, therefore, necessary to establish a suitable criterion for the replacement period of chevron rubber spring. In this study, we performed characteristic analysis and useful lifetime prediction of chevron rubber spring. Rubber material coefficient was obtained by curve fittings of uni-axial tension, equi bi-axial tension and pure shear test. Computer simulation was executed to predict and evaluate the load capacity and stiffness for chevron rubber spring. In order to useful lifetime prediction of rubber material, we carried out the compression set with heat aging test in an oven at the temperature ranging from 50°C to 100°C during a period 180 days. By using the Arrhenius plot, several useful lifetime prediction equations for rubber material was proposed.

Keywords: chevron rubber spring, material coefficient, finite element analysis, useful lifetime prediction

Procedia PDF Downloads 568

Authors: Ellis D. Cooper

Abstract:

“Circularchy” is supposed to be an adjustable formal framework with enough expressive power to articulate biological theory about Earthly Life in the sense of multi-scale biological autonomy constrained by non-equilibrium thermodynamics. “Formal framework” means specifically a multi-sorted first-order-theorywithequality (for each sort). Philosophically, such a theory is one kind of “microlect,” which means a “way of speaking” (or, more generally, a “way of behaving”) for overtly expressing a “mental model” of some “referent.” Other kinds of microlect include “natural microlect,” “diagrammatic microlect,” and “behavioral microlect,” with examples such as “political theory,” “Euclidean geometry,” and “dance choreography,” respectively. These are all describable in terms of a vocabulary conforming to grammar. As aspects of human culture, they are possibly reminiscent of Ernst Cassirer’s idea of “symbolic form;” as vocabularies, they are akin to Richard Rorty’s idea of “final vocabulary” for expressing a mental model of one’s life. A formal microlect is presented by stipulating sorts, variables, calculations, predicates, and postulates. Calculations (a.k.a., “terms”) may be composed to form more complicated calculations; predicates (a.k.a., “relations”) may be logically combined to form more complicated predicates; and statements (a.k.a., “sentences”) are grammatically correct expressions which are true or false. Conclusions are statements derived using logical rules of deduction from postulates, other assumed statements, or previously derived conclusions. A circularchy is a formal microlect constituted by two or more sub-microlects, each with its distinct stipulations of sorts, variables, calculations, predicates, and postulates. Within a sub-microlect some postulates or conclusions are equations which are statements that declare equality of specified calculations. An equational bond between an equation in one sub-microlect and an equation in either the same sub-microlect or in another sub-microlect is a predicate that declares equality of symbols occurring in a side of one equation with symbols occurring in a side of the other equation. Briefly, a circularchy is a network of equational bonds between sub-microlects. A circularchy is solvable if there exist solutions for all equations that satisfy all equational bonds. If a circularchy is not solvable, then a challenge would be to discover the obstruction to solvability and then conjecture what adjustments might remove the obstruction. Adjustment means changes in stipulated ingredients (sorts, etc.) of sub-microlects, or changes in equational bonds between sub-microlects, or introduction of new sub-microlects and new equational bonds. A circularchy is modular insofar as each sub-microlect is a node in a network of equation bonds. Solvability of a circularchy may be conjectured. Efforts to prove solvability may be thwarted by a counter-example or may lead to the construction of a solution. An automated theorem-proof assistant would likely be necessary for investigating a substantial circularchy, such as one purported to represent Earthly Life. Such investigations (chains of statements) would be concurrent with and no substitute for simulations (chains of numbers).

Keywords: autonomy, first-order theory, mathematics, thermodynamics

Procedia PDF Downloads 221

Authors: Amira Amamou, Mnaouar Chouchane

Abstract:

This paper investigates the bifurcation and nonlinear behavior of two degrees of freedom model of a symmetrical balanced rigid rotor supported by two identical journal bearings. The fluid film hydrodynamic reactions are modeled by applying both the short and the long bearing approximation and using half Sommerfeld solution. A numerical integration of equations of the journal centre motion is presented to predict the presence and the size of stable or unstable limit cycles in the neighborhood of the stability critical speed. For their stability margins, a continuation method based on the predictor-corrector mechanism is used. The numerical results of responses show that stability and bifurcation behaviors of periodic motions depend strongly on bearing parameters and its dynamic characteristics.

Keywords: hydrodynamic journal bearing, nonlinear stability, continuation method, bifurcations

Procedia PDF Downloads 409

Authors: Muhammad Asghar Saqib, Saad Saleem Khan, Syed Abdul Rahman Kashif

Abstract:

In order to have higher efficiency, performance and reliability the regular monitoring of an electrical motor is required. This article presents a novel view of the air-gap magnetic field analysis of a switched reluctance motor under rotor cracks and rotor tilt along its shaft axis. The fault diagnosis is illustrated on the basis of a 3-D model of the motor using finite element analysis (FEA). The analytical equations of flux linkages have been used to determine the inductance. The results of the 3-D finite element analysis on a 6/4 switched reluctance motor (SRM) shows the variation of mutual inductance with the tilting of the rotor shaft and cracked rotor conditions. These results present useful information regarding the detection of shaft tilting and cracked rotors.

Keywords: switched reluctance motor, finite element analysis, cracked rotor, 3-D modelling of a srm

Procedia PDF Downloads 667

Authors: M. Guemmadi, A. Ouibrahim

Abstract:

This numerical investigation aims to evaluate how a viscoelastic lubricant described by a generalized Maxwell model, affects the pressure distribution, the load capacity and thermal effect in a journal bearing lubrication. We use for the purpose the CFD package software completed by adapted user define functions (UDFs) to solve the coupled equations of momentum, of energy and of the viscoelastic model (generalized Maxwell model). Two parameters, viscosity and relaxation time are involved to show how viscoelasticity substantially affect the pressure distribution, the load capacity and the thermal transfer by comparison to Newtonian lubricant. These results were also compared with the available published results.

Keywords: journal bearing, lubrication, Maxwell model, viscoelastic fluids, computational modelling, load capacity

Procedia PDF Downloads 542

Authors: Brahim Mahfoud, Rachid Bessaïh

Abstract:

In this paper, a numerical study of steady and oscillatory flows with heat transfer submitted to an axial magnetic field is studied. The governing Navier-Stokes, energy, and potential equations along with appropriate boundary conditions are solved by using the finite-volume method. The flow and temperature fields are presented by stream function and isotherms, respectively. The flow between counter-rotating end disks is very unstable and reveals a great richness of structures. The results are presented for various values of the Hartmann number, Ha=5, 10, 20, and 30, and Richardson numbers , Ri=0, 0.5, 1, 2, and 4, in order to see their effects on the value of the critical Reynolds number, Recr. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of Recr with the increase of Ha for various values of Ri.

Keywords: swirling, counter-rotating end disks, magnetic field, oscillatory, cylinder

Procedia PDF Downloads 325

Authors: Mohammad Reza Akhavan Khaleghi

Abstract:

This paper shows changes done to the Reduced Finite Element Method (RFEM) that its result will be the most powerful numerical method that has been proposed so far (some forms of this method are so powerful that they can approximate the most complex equations simply Laplace equation!). Finite Element Method (FEM) is a powerful numerical method that has been used successfully for the solution of the existing problems in various scientific and engineering fields such as its application in CFD. Many algorithms have been expressed based on FEM, but none have been used in popular CFD software. In this section, full monopoly is according to Finite Volume Method (FVM) due to better efficiency and adaptability with the physics of problems in comparison with FEM. It doesn't seem that FEM could compete with FVM unless it was fundamentally changed. This paper shows those changes and its result will be a powerful method that has much better performance in all subjects in comparison with FVM and another computational method. This method is not to compete with the finite volume method but to replace it.

Keywords: reduced finite element method, new computational package, new finite element formulation, new higher-order form, new isogeometric analysis

Procedia PDF Downloads 119

Authors: Thana Ananacha

Abstract:

This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered namely 400 and 800 W.m-2 the corresponding initial condition temperatures were to 30.5 and 38.5 ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: thermal simulation, Double Glass Wall, velocity field, finite element method (FEM)

Procedia PDF Downloads 359

Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

Abstract:

We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: indentation, contact problem, stress distribution, coating materials, layer-substrate body

Procedia PDF Downloads 156

Authors: Fatemeh Faramarzi, Hosein Mahjoob

Abstract:

Building dams on rivers for utilization of water resources causes problems in hydrodynamic equilibrium and results in leaving all or part of the sediments carried by water in dam reservoir. This phenomenon has also significant impacts on water and sediment flow regime and in the long term can cause morphological changes in the environment surrounding the river, reducing the useful life of the reservoir which threatens sustainable development through inefficient management of water resources. In the past, empirical methods were used to predict the sedimentation amount in dam reservoirs and to estimate its efficient lifetime. But recently the mathematical and computational models are widely used in sedimentation studies in dam reservoirs as a suitable tool. These models usually solve the equations using finite element method. This study compares the results from tow software packages, GSTARS4 & HEC-6, in the prediction of the sedimentation amount in Dez dam, southern Iran. The model provides a one-dimensional, steady-state simulation of sediment deposition and erosion by solving the equations of momentum, flow and sediment continuity and sediment transport. GSTARS4 (Generalized Sediment Transport Model for Alluvial River Simulation) which is based on a one-dimensional mathematical model that simulates bed changes in both longitudinal and transverse directions by using flow tubes in a quasi-two-dimensional scheme to calibrate a period of 47 years and forecast the next 47 years of sedimentation in Dez Dam, Southern Iran. This dam is among the highest dams all over the world (with its 203 m height), and irrigates more than 125000 square hectares of downstream lands and plays a major role in flood control in the region. The input data including geometry, hydraulic and sedimentary data, starts from 1955 to 2003 on a daily basis. To predict future river discharge, in this research, the time series data were assumed to be repeated after 47 years. Finally, the obtained result was very satisfactory in the delta region so that the output from GSTARS4 was almost identical to the hydrographic profile in 2003. In the Dez dam due to the long (65 km) and a large tank, the vertical currents are dominant causing the calculations by the above-mentioned method to be inaccurate. To solve this problem, we used the empirical reduction method to calculate the sedimentation in the downstream area which led to very good answers. Thus, we demonstrated that by combining these two methods a very suitable model for sedimentation in Dez dam for the study period can be obtained. The present study demonstrated successfully that the outputs of both methods are the same.

Keywords: Dez Dam, prediction, sedimentation, water resources, computational models, finite element method, GSTARS4, HEC-6

Procedia PDF Downloads 313