Search results for: degenerate parabolic equations
1461 Normal Spectral Emissivity of Roughened Aluminum Alloy AL 6061 Surfaces at High Temperature
Authors: Sumeet Kumar, C. V. Krishnamurthy, Krishnan Balasubramaniam
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Normal spectral emissivity of Al 6061 alloys with different surface finishes was experimentally measured at 833°K. Four different samples were prepared by polishing the surfaces of the alloy by 80, 220, 600 grit sizes of SiC abrasive papers and diamond paste. The samples were heated in air for 6 h at 833°K, and the emissivity was measured during the process from pyrometers operating at wavelengths of 3.9, 5.14 and 7.8 μm. The results indicated that the emissivity was increasing with heating time and the rate of increase was rapid during the initial stage of heating in comparison with the later stage. This appears to be because of the parabolic rate law followed by the process of oxidation. Further, it is found that the increase in emissivity with heating time was higher for rough surfaces than that for polished surfaces. Both the results were analyzed at all the three wavelengths, and qualitatively similar results were obtained for all of them. In this way emissivity of the alloy can be increased by roughening the surfaces and heating it at high temperature until the surfaces are oxidized.Keywords: aluminum alloy, high temperature, normal spectral emissivity, surface roughness
Procedia PDF Downloads 2171460 Effect of Thermal Radiation and Chemical Reaction on MHD Flow of Blood in Stretching Permeable Vessel
Authors: Binyam Teferi
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In this paper, a theoretical analysis of blood flow in the presence of thermal radiation and chemical reaction under the influence of time dependent magnetic field intensity has been studied. The unsteady non linear partial differential equations of blood flow considers time dependent stretching velocity, the energy equation also accounts time dependent temperature of vessel wall, and concentration equation includes time dependent blood concentration. The governing non linear partial differential equations of motion, energy, and concentration are converted into ordinary differential equations using similarity transformations solved numerically by applying ode45. MATLAB code is used to analyze theoretical facts. The effect of physical parameters viz., permeability parameter, unsteadiness parameter, Prandtl number, Hartmann number, thermal radiation parameter, chemical reaction parameter, and Schmidt number on flow variables viz., velocity of blood flow in the vessel, temperature and concentration of blood has been analyzed and discussed graphically. From the simulation study, the following important results are obtained: velocity of blood flow increases with both increment of permeability and unsteadiness parameter. Temperature of the blood increases in vessel wall as Prandtl number and Hartmann number increases. Concentration of the blood decreases as time dependent chemical reaction parameter and Schmidt number increases.Keywords: stretching velocity, similarity transformations, time dependent magnetic field intensity, thermal radiation, chemical reaction
Procedia PDF Downloads 851459 Numerical Studies for Standard Bi-Conjugate Gradient Stabilized Method and the Parallel Variants for Solving Linear Equations
Authors: Kuniyoshi Abe
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Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant
Procedia PDF Downloads 1551458 Linearization of Y-Force Equation of Rigid Body Equation of Motion and Behavior of Fighter Aircraft under Imbalance Weight on Wings during Combat
Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood
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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion
Procedia PDF Downloads 4911457 Importance of Mathematical Modeling in Teaching Mathematics
Authors: Selahattin Gultekin
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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling
Procedia PDF Downloads 3111456 Ultrafast Ground State Recovery Dynamics of a Cyanine Dye Molecule in Heterogeneous Environment
Authors: Tapas Goswami, Debabrata Goswami
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We have studied the changes in ground state recovery dynamics of IR 144 dye using degenerate transient absorption spectroscopy technique when going from homogeneous solution phase to heterogeneous partially miscible liquid/liquid interface. Towards this aim, we set up a partially miscible liquid/liquid interface in which dye is insoluble in one solvent carbon tetrachloride (CCl₄) layer and soluble in other solvent dimethyl sulphoxide (DMSO). A gradual increase in ground state recovery time of the dye molecule is observed from homogenous bulk solution to more heterogeneous environment interface layer. In the bulk solution charge distribution of dye molecule is in equilibrium with polar DMSO solvent molecule. Near the interface micro transportation of non-polar solvent, CCl₄ disturbs the solvent equilibrium in DMSO layer and it relaxes to a new equilibrium state corresponding to a new charge distribution of dye with a heterogeneous mixture of polar and non-polar solvent. In this experiment, we have measured the time required for the dye molecule to relax to the new equilibrium state in different heterogeneous environment. As a result, dye remains longer time in the excited state such that even it can populate more triplet state. The present study of ground state recovery dynamics of a cyanine dye molecule in different solvent environment provides the important characteristics of effect of solvation on excited life time of a dye molecule.Keywords: excited state, ground state recovery, solvation, transient absorption
Procedia PDF Downloads 2761455 Performance Study of Scraped Surface Heat Exchanger with Helical Ribbons
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In this work, numerical simulations were carried out using a specific CFD code in order to study the performance of an innovative Scraped Surface Heat Exchanger (SSHE) with helical ribbons for Bingham fluids (threshold fluids). The resolution of three-dimensional form of the conservation equations (continuity, momentum and energy equations) was carried out basing on the finite volume method (FVM). After studying the effect of dimensionless numbers (axial Reynolds, rotational Reynolds and Oldroyd numbers) on the hydrodynamic and thermal behaviors within SSHE, a parametric study was developed, by varying the width of the helical ribbon, the clearance between the stator wall and the tip of the ribbon and the number of turns of the helical ribbon, in order to improve the heat transfer inside the exchanger. The effect of these geometrical numbers on the hydrodynamic and thermal behaviors was discussed.Keywords: heat transfer, helical ribbons, hydrodynamic behavior, parametric study, SSHE, thermal behavior
Procedia PDF Downloads 2101454 Computational Code for Solving the Navier-Stokes Equations on Unstructured Meshes Applied to the Leading Edge of the Brazilian Hypersonic Scramjet 14-X
Authors: Jayme R. T. Silva, Paulo G. P. Toro, Angelo Passaro, Giannino P. Camillo, Antonio C. Oliveira
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An in-house C++ code has been developed, at the Prof. Henry T. Nagamatsu Laboratory of Aerothermodynamics and Hypersonics from the Institute of Advanced Studies (Brazil), to estimate the aerothermodynamic properties around the Hypersonic Vehicle Integrated to the Scramjet. In the future, this code will be applied to the design of the Brazilian Scramjet Technological Demonstrator 14-X B. The first step towards accomplishing this objective, is to apply the in-house C++ code at the leading edge of a flat plate, simulating the leading edge of the 14-X Hypersonic Vehicle, making possible the wave phenomena of oblique shock and boundary layer to be analyzed. The development of modern hypersonic space vehicles requires knowledge regarding the characteristics of hypersonic flows in the vicinity of a leading edge of lifting surfaces. The strong interaction between a shock wave and a boundary layer, in a high supersonic Mach number 4 viscous flow, close to the leading edge of the plate, considering no slip condition, is numerically investigated. The small slip region is neglecting. The study consists of solving the fluid flow equations for unstructured meshes applying the SIMPLE algorithm for Finite Volume Method. Unstructured meshes are generated by the in-house software ‘Modeler’ that was developed at Virtual’s Engineering Laboratory from the Institute of Advanced Studies, initially developed for Finite Element problems and, in this work, adapted to the resolution of the Navier-Stokes equations based on the SIMPLE pressure-correction scheme for all-speed flows, Finite Volume Method based. The in-house C++ code is based on the two-dimensional Navier-Stokes equations considering non-steady flow, with nobody forces, no volumetric heating, and no mass diffusion. Air is considered as calorically perfect gas, with constant Prandtl number and Sutherland's law for the viscosity. Solutions of the flat plate problem for Mach number 4 include pressure, temperature, density and velocity profiles as well as 2-D contours. Also, the boundary layer thickness, boundary conditions, and mesh configurations are presented. The same problem has been solved by the academic license of the software Ansys Fluent and for another C++ in-house code, which solves the fluid flow equations in structured meshes, applying the MacCormack method for Finite Difference Method, and the results will be compared.Keywords: boundary-layer, scramjet, simple algorithm, shock wave
Procedia PDF Downloads 4791453 The Channels through Which Energy Tax Can Affect Economic Growth: Panel Data Analysis
Authors: Mahmoud Hassan, Walid Oueslati, Damien Rousseliere
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This paper explores the channels through which energy taxes may affect economic growth, using a simultaneous equations model for a balanced panel data of 31 OECD countries over the 1994–2013 period. The empirical results reveal a negative impact of energy taxes on physical investment in the short and long term. This impact is negatively sensitive to the existence and level of public debt. Additionally, the results show that energy taxes have an indirect effect on human capital through their impact on polluting emissions. The taxes on energy products are able to reduce both the flux and the stock of polluting emissions that have a negative impact on human capital skills in the short and long term. Finally, we found that energy taxes could encourage eco-innovation in the short and long term.Keywords: energy taxes, economic growth, public debt, simultaneous equations model, multiple imputation
Procedia PDF Downloads 2271452 Application of Regularized Spatio-Temporal Models to the Analysis of Remote Sensing Data
Authors: Salihah Alghamdi, Surajit Ray
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Space-time data can be observed over irregularly shaped manifolds, which might have complex boundaries or interior gaps. Most of the existing methods do not consider the shape of the data, and as a result, it is difficult to model irregularly shaped data accommodating the complex domain. We used a method that can deal with space-time data that are distributed over non-planner shaped regions. The method is based on partial differential equations and finite element analysis. The model can be estimated using a penalized least squares approach with a regularization term that controls the over-fitting. The model is regularized using two roughness penalties, which consider the spatial and temporal regularities separately. The integrated square of the second derivative of the basis function is used as temporal penalty. While the spatial penalty consists of the integrated square of Laplace operator, which is integrated exclusively over the domain of interest that is determined using finite element technique. In this paper, we applied a spatio-temporal regression model with partial differential equations regularization (ST-PDE) approach to analyze a remote sensing data measuring the greenness of vegetation, measure by an index called enhanced vegetation index (EVI). The EVI data consist of measurements that take values between -1 and 1 reflecting the level of greenness of some region over a period of time. We applied (ST-PDE) approach to irregular shaped region of the EVI data. The approach efficiently accommodates the irregular shaped regions taking into account the complex boundaries rather than smoothing across the boundaries. Furthermore, the approach succeeds in capturing the temporal variation in the data.Keywords: irregularly shaped domain, partial differential equations, finite element analysis, complex boundray
Procedia PDF Downloads 1361451 Investigating the Effects of Thermal and Surface Energy on the Two-Dimensional Flow Characteristics of Oil in Water Mixture between Two Parallel Plates: A Lattice Boltzmann Method Study
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A hybrid quasi-steady thermal lattice Boltzmann model was used to study the combined effects of temperature and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain’s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably.Keywords: lattice Boltzmann method, Gunstensen model, thermal, contact angle, high viscosity ratio
Procedia PDF Downloads 3601450 Prediction of Maximum Inter-Story Drifts of Steel Frames Using Intensity Measures
Authors: Edén Bojórquez, Victor Baca, Alfredo Reyes-Salazar, Jorge González
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In this paper, simplified equations to predict maximum inter-story drift demands of steel framed buildings are proposed in terms of two ground motion intensity measures based on the acceleration spectral shape. For this aim, the maximum inter-story drifts of steel frames with 4, 6, 8 and 10 stories subjected to narrow-band ground motion records are estimated and compared with the spectral acceleration at first mode of vibration Sa(T1) which is commonly used in earthquake engineering and seismology, and with a new parameter related with the structural response known as INp. It is observed that INp is the parameter best related with the structural response of steel frames under narrow-band motions. Finally, equations to compute maximum inter-story drift demands of steel frames as a function of spectral acceleration and INp are proposed.Keywords: intensity measures, spectral shape, steel frames, peak demands
Procedia PDF Downloads 3851449 Stochastic Matrices and Lp Norms for Ill-Conditioned Linear Systems
Authors: Riadh Zorgati, Thomas Triboulet
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In quite diverse application areas such as astronomy, medical imaging, geophysics or nondestructive evaluation, many problems related to calibration, fitting or estimation of a large number of input parameters of a model from a small amount of output noisy data, can be cast as inverse problems. Due to noisy data corruption, insufficient data and model errors, most inverse problems are ill-posed in a Hadamard sense, i.e. existence, uniqueness and stability of the solution are not guaranteed. A wide class of inverse problems in physics relates to the Fredholm equation of the first kind. The ill-posedness of such inverse problem results, after discretization, in a very ill-conditioned linear system of equations, the condition number of the associated matrix can typically range from 109 to 1018. This condition number plays the role of an amplifier of uncertainties on data during inversion and then, renders the inverse problem difficult to handle numerically. Similar problems appear in other areas such as numerical optimization when using interior points algorithms for solving linear programs leads to face ill-conditioned systems of linear equations. Devising efficient solution approaches for such system of equations is therefore of great practical interest. Efficient iterative algorithms are proposed for solving a system of linear equations. The approach is based on a preconditioning of the initial matrix of the system with an approximation of a generalized inverse leading to a stochastic preconditioned matrix. This approach, valid for non-negative matrices, is first extended to hermitian, semi-definite positive matrices and then generalized to any complex rectangular matrices. The main results obtained are as follows: 1) We are able to build a generalized inverse of any complex rectangular matrix which satisfies the convergence condition requested in iterative algorithms for solving a system of linear equations. This completes the (short) list of generalized inverse having this property, after Kaczmarz and Cimmino matrices. Theoretical results on both the characterization of the type of generalized inverse obtained and the convergence are derived. 2) Thanks to its properties, this matrix can be efficiently used in different solving schemes as Richardson-Tanabe or preconditioned conjugate gradients. 3) By using Lp norms, we propose generalized Kaczmarz’s type matrices. We also show how Cimmino's matrix can be considered as a particular case consisting in choosing the Euclidian norm in an asymmetrical structure. 4) Regarding numerical results obtained on some pathological well-known test-cases (Hilbert, Nakasaka, …), some of the proposed algorithms are empirically shown to be more efficient on ill-conditioned problems and more robust to error propagation than the known classical techniques we have tested (Gauss, Moore-Penrose inverse, minimum residue, conjugate gradients, Kaczmarz, Cimmino). We end on a very early prospective application of our approach based on stochastic matrices aiming at computing some parameters (such as the extreme values, the mean, the variance, …) of the solution of a linear system prior to its resolution. Such an approach, if it were to be efficient, would be a source of information on the solution of a system of linear equations.Keywords: conditioning, generalized inverse, linear system, norms, stochastic matrix
Procedia PDF Downloads 1271448 Load Maximization of Two-Link Flexible Manipulator Using Suppression Vibration with Piezoelectric Transducer
Authors: Hamidreza Heidari, Abdollah Malmir Nasab
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In this paper, the energy equations of a two-link flexible manipulator were extracted using the Euler-Bernoulli beam hypotheses. Applying Assumed mode and considering some finite degrees of freedom, we could obtain dynamic motions of each manipulator using Euler-Lagrange equations. Using its claws, the robots can carry a certain load with the ached control of vibrations for robot flexible links during the travelling path using the piezoceramics transducer; dynamic load carrying capacity increase. The traveling path of flexible robot claw has been taken from that of equivalent rigid manipulator and coupled; therefore to avoid the role of Euler-Bernoulli beam assumptions and linear strains, material and physical characteristics selection of robot cause deflection of link ends not exceed 5% of link length. To do so, the maximum load carrying capacity of robot is calculated at the horizontal plan. The increasing of robot load carrying capacity with vibration control is 53%.Keywords: flexible link, DLCC, active control vibration, assumed mode method
Procedia PDF Downloads 3881447 Performance Modeling and Availability Analysis of Yarn Dyeing System of a Textile Industry
Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja
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This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are, therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.Keywords: performance modeling, markov process, steady state availability, availability analysis
Procedia PDF Downloads 3281446 Modeling and Optimization of Performance of Four Stroke Spark Ignition Injector Engine
Authors: A. A. Okafor, C. H. Achebe, J. L. Chukwuneke, C. G. Ozoegwu
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The performance of an engine whose basic design parameters are known can be predicted with the assistance of simulation programs into the less time, cost and near value of actual. This paper presents a comprehensive mathematical model of the performance parameters of four stroke spark ignition engine. The essence of this research work is to develop a mathematical model for the analysis of engine performance parameters of four stroke spark ignition engine before embarking on full scale construction, this will ensure that only optimal parameters are in the design and development of an engine and also allow to check and develop the design of the engine and it’s operation alternatives in an inexpensive way and less time, instead of using experimental method which requires costly research test beds. To achieve this, equations were derived which describe the performance parameters (sfc, thermal efficiency, mep and A/F). The equations were used to simulate and optimize the engine performance of the model for various engine speeds. The optimal values obtained for the developed bivariate mathematical models are: sfc is 0.2833kg/kwh, efficiency is 28.77% and a/f is 20.75.Keywords: bivariate models, engine performance, injector engine, optimization, performance parameters, simulation, spark ignition
Procedia PDF Downloads 3191445 Verification and Application of Finite Element Model Developed for Flood Routing in Rivers
Authors: A. L. Qureshi, A. A. Mahessar, A. Baloch
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Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. However, it is difficult to find analytical solution of these complex non-linear equations. Hence, verification of the numerical model should be carried out against field data and numerical predictions. This paper presents the verification of developed finite element model applying for unsteady flow in the open channels. The results of a proposed model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29 km at both sites (15 km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400 km downstream from Sukkur barrage, which demonstrates accurate model predictions with observed daily discharges. Hence, this model may be utilized for predicting and issuing flood warnings about flood hazardous in advance.Keywords: finite element method, Preissmann scheme, HEC-RAS, flood forecasting, Indus river
Procedia PDF Downloads 4961444 Model Order Reduction of Continuous LTI Large Descriptor System Using LRCF-ADI and Square Root Balanced Truncation
Authors: Mohammad Sahadet Hossain, Shamsil Arifeen, Mehrab Hossian Likhon
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In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives low-rank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems.Keywords: low-rank cholesky factor alternating directions implicit iteration, LTI Descriptor system, Lyapunov equations, Square-root balanced truncation
Procedia PDF Downloads 4131443 The Incompressible Preference of Turbulence
Authors: Samuel David Dunstan
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An elementary observation of a laminar cylindrical Poiseulle-Couette flow profile reveals no distinction in the parabolic streamwise profile from one without a cross-stream flow in whatever reference frame the observation is made. This is because the laminar flow is in solid-body rotation, and there is no intrinsic fluid rotation. Hence the main streamwise Poiseuille flow is unaffected. However, in turbulent (unsteady) cylindrical Poiseuille-Couette flow, the rotational reference frame must be considered, and any observation from an external inertial reference frame can give outright incorrect results. A common misconception in the study of fluid mechanics is the position of the observer does not matter. In this DNS (direct numerical simulation) study, firstly, turbulent flow in a pipe with axial rotation is established. Then in turbulent flow in the concentric pipe, with inner wall rotation, it is shown how the wall streak direction is oriented by the rotational reference frame. The Coriolis force here is not so fictitious after all!Keywords: concentric pipe, rotational and inertial frames, frame invariance, wall streaks, flow orientation
Procedia PDF Downloads 841442 An Inviscid Compressible Flow Solver Based on Unstructured OpenFOAM Mesh Format
Authors: Utkan Caliskan
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Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach.Keywords: cell centered finite volume method, compressible Euler equations, OpenFOAM mesh format, OpenMP
Procedia PDF Downloads 3121441 Comparison of Conventional Control and Robust Control on Double-Pipe Heat Exchanger
Authors: Hanan Rizk
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A heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed a PID controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software, and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control
Procedia PDF Downloads 2151440 Effect of Footing Shape on Bearing Capacity and Settlement of Closely Spaced Footings on Sandy Soil
Authors: A. Shafaghat, H. Khabbaz, S. Moravej, Ah. Shafaghat
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The bearing capacity of closely spaced shallow footings alters with their spacing and the shape of footing. In this study, the bearing capacity and settlement of two adjacent footings constructed on a sand layer are investigated. The effect of different footing shapes including square, circular, ring and strip on sandy soil is captured in the calculations. The investigations are carried out numerically using PLAXIS-3D software and analytically employing conventional settlement equations. For this purpose, foundations are modelled in the program with practical dimensions and various spacing ratios ranging from 1 to 5. The spacing ratio is defined as the centre-to-centre distance to the width of foundations (S/B). Overall, 24 models are analyzed; and the results are compared and discussed in detail. It can be concluded that the presence of adjacent foundation leads to the reduction in bearing capacity for round shape footings while it can increase the bearing capacity of rectangular footings in some specific distances.Keywords: bearing capacity, finite element analysis, loose sand, settlement equations, shallow foundation
Procedia PDF Downloads 2521439 Energy Dynamics of Solar Thermionic Power Conversion with Emitter of Graphene
Authors: Olukunle C. Olawole, Dilip K. De, Moses Emetere, Omoje Maxwell
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Graphene can stand very high temperature up to 4500 K in vacuum and has potential for application in thermionic energy converter. In this paper, we discuss the application of energy dynamics principles and the modified Richardson-Dushman Equation, to estimate the efficiency of solar power conversion to electrical power by a solar thermionic energy converter (STEC) containing emitter made of graphene. We present detailed simulation of power output for different solar insolation, diameter of parabolic concentrator, area of the graphene emitter (same as that of the collector), temperature of the collector, physical dimensions of the emitter-collector etc. After discussing possible methods of reduction or elimination of space charge problem using magnetic field and gate, we finally discuss relative advantages of using emitters made of graphene, carbon nanotube and metals respectively in a STEC.Keywords: graphene, high temperature, modified Richardson-Dushman equation, solar thermionic energy converter
Procedia PDF Downloads 3021438 The Improved Laplace Homotopy Perturbation Method for Solving Non-integrable PDEs
Authors: Noufe H. Aljahdaly
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The Laplace homotopy perturbation method (LHPM) is an approximate method that help to compute the approximate solution for partial differential equations. The method has been used for solving several problems in science. It requires the initial condition, so it solves the initial value problem. In physics, when some important terms are taken in account, we may obtain non-integrable partial differential equations that do not have analytical integrals. This type of PDEs do not have exact solution, therefore, we need to compute the solution without initial condition. In this work, we improved the LHPM to be able to solve non-integrable problem, especially the damped PDEs, which are the PDEs that include a damping term which makes the PDEs non-integrable. We improved the LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for damped PDE as the initial condition for non-damped PDE.Keywords: non-integrable PDEs, modified Kawahara equation;, laplace homotopy perturbation method, damping term
Procedia PDF Downloads 901437 Magneto-Hydrodynamic Mixed Convective Fluid Flow through Two Parallel Vertical Plates Channel with Hall, Chemical Reaction, and Thermal Radiation Effects
Authors: Okuyade Ighoroje Wilson Ata
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Magneto-hydrodynamic mixed convective chemically reacting fluid flow through two parallel vertical plates channel with Hall, radiation, and chemical reaction effects are examined. The fluid is assumed to be chemically reactive, electrically conducting, magnetically susceptible, viscous, incompressible, and Newtonian; the plates are porous, electrically conductive, and heated to a high-temperature regime to generate thermal rays. The flow system is highly interactive, such that cross/double diffusion is present. The governing equations are partial differential equations transformed into ordinary differential equations using similarity transformation and solved by the method of Homotopy Perturbation. Expressions for the concentration, temperature, velocity, Nusselt number, Sherwood number, and Wall shear stress are obtained, computed, and presented graphically and tabularly. The analysis of results shows, amongst others, that an increase in the Raleigh number increases the main velocity and temperature but decreases the concentration. More so, an increase in chemical reaction rate increases the main velocity, temperature, rate of heat transfer from the terminal plate, the rate of mass transfer from the induced plate, and Wall shear stress on both the induced and terminal plates, decreasing the concentration, and the mass transfer rate from the terminal plate. Some of the obtained results are benchmarked with those of existing literature and are in consonance.Keywords: chemical reaction, hall effect, magneto-hydrodynamic, radiation, vertical plates channel
Procedia PDF Downloads 711436 Traction Behavior of Linear Piezo-Viscous Lubricants in Rough Elastohydrodynamic Lubrication Contacts
Authors: Punit Kumar, Niraj Kumar
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The traction behavior of lubricants with the linear pressure-viscosity response in EHL line contacts is investigated numerically for smooth as well as rough surfaces. The analysis involves the simultaneous solution of Reynolds, elasticity and energy equations along with the computation of lubricant properties and surface temperatures. The temperature modified Doolittle-Tait equations are used to calculate viscosity and density as functions of fluid pressure and temperature, while Carreau model is used to describe the lubricant rheology. The surface roughness is assumed to be sinusoidal and it is present on the nearly stationary surface in near-pure sliding EHL conjunction. The linear P-V oil is found to yield much lower traction coefficients and slightly thicker EHL films as compared to the synthetic oil for a given set of dimensionless speed and load parameters. Besides, the increase in traction coefficient attributed to surface roughness is much lower for the former case. The present analysis emphasizes the importance of employing realistic pressure-viscosity response for accurate prediction of EHL traction.Keywords: EHL, linear pressure-viscosity, surface roughness, traction, water/glycol
Procedia PDF Downloads 3781435 Microstructure and Oxidation Behaviors of Al, Y Modified Silicide Coatings Prepared on an Nb-Si Based Ultrahigh Temperature Alloy
Authors: Xiping Guo, Jing Li
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The microstructure of an Si-Al-Y co-deposition coating prepared on an Nb-Si based ultra high temperature alloy by pack cementation process at 1250°C for eight hours was studied. The results showed that the coating was composed of a (Nb,X)Si₂ (X represents Ti, Cr and Hf elements) outer layer, a (Ti,Nb)₅Si₄ middle layer and an Al, Cr-rich inner layer. For comparison, the oxidation behaviors of the coating at 800, 1050 and 1350°C were investigated respectively. Linear oxidation kinetics was found with the parabolic rate constants of 5.29×10⁻², 9×10⁻²and 5.81 mg² cm⁻⁴ h⁻¹, respectively. Catastrophic pesting oxidation has not been found at 800°C even for 100 h. The surface of the scale was covered by compact glassy SiO₂ film. The coating was able to effectively protect the Nb-Si based alloy from oxidation at 1350°C for at least 100 h. The formation process of the scale was testified following an epitaxial growth mechanism. The mechanism responsible for the oxidation behavior of the Si-Al-Y co-deposition coating at 800, 1050 and 1350°C was proposed.Keywords: Nb-Si based ultra high temperature alloy, oxidation resistance, pack cementation, silicide coating, Al and Y modified
Procedia PDF Downloads 3941434 Anharmonic Behavior in BaTiO3: Investigation by Raman Spectroscopy
Authors: M. D. Fontana, I. Bejaoui Ouni, D. Chapron, H. Aroui
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BaTiO3 (BT) is a well known ferroelectric material which has been thoroughly studied during several decades since it undergoes successive cubic-tetragonal-orthorhombic-rhombohedral phase transitions on cooling. It has several ferroelectric properties that allow it to be a good material for electronic applications such as the design of ferroelectric memories and pyroelectric elements. In the present work, we report the analysis of temperature dependence of Raman frequency and damping of the A1 modes polarized along the FE c axis as well as the optical phonons E corresponding to the ionic motions in the plane normal to c. Measurements were carried out at different temperatures ranging from 298 to 408 K (tetragonal phase) within different scattering configurations. Spectroscopic parameters of BT have determined using a high resolution Raman spectrometer and a fitting program. All the first order frequency modes exhibit a quasi linear decrease as function of the temperature, except for the A1[TO1], E[TO2] and E[TO4] lines which reveal a parabolic dependence illustrating an anharmonic process. The phonon frequency downshifts and damping evolutions are interpreted in terms of normal volume expansion and third- and fourth-order anharmonic potentials.Keywords: BaTiO3, Raman spectroscopy, frequency, damping, anharmonic potential
Procedia PDF Downloads 2951433 Fault-Detection and Self-Stabilization Protocol for Wireless Sensor Networks
Authors: Ather Saeed, Arif Khan, Jeffrey Gosper
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Sensor devices are prone to errors and sudden node failures, which are difficult to detect in a timely manner when deployed in real-time, hazardous, large-scale harsh environments and in medical emergencies. Therefore, the loss of data can be life-threatening when the sensed phenomenon is not disseminated due to sudden node failure, battery depletion or temporary malfunctioning. We introduce a set of partial differential equations for localizing faults, similar to Green’s and Maxwell’s equations used in Electrostatics and Electromagnetism. We introduce a node organization and clustering scheme for self-stabilizing sensor networks. Green’s theorem is applied to regions where the curve is closed and continuously differentiable to ensure network connectivity. Experimental results show that the proposed GTFD (Green’s Theorem fault-detection and Self-stabilization) protocol not only detects faulty nodes but also accurately generates network stability graphs where urgent intervention is required for dynamically self-stabilizing the network.Keywords: Green’s Theorem, self-stabilization, fault-localization, RSSI, WSN, clustering
Procedia PDF Downloads 691432 Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian
Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma
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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental
Procedia PDF Downloads 203