Search results for: nonlinear Takagi’s equations

Authors: Woo Young Jung, Min Ho Kwon, Bu Seog Ju

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A failure of the non-structural component can cause significant damages in critical facilities such as nuclear power plants and hospitals. Historically, it was reported that the damage from the leakage of sprinkler systems, resulted in the shutdown of hospitals for several weeks by the 1971 San Fernando and 1994 North Ridge earthquakes. In most cases, water leakages were observed at the cross joints, sprinkler heads, and T-joint connections in piping systems during and after the seismic events. Hence, the primary objective of this study was to understand the seismic performance of T-joint connections and to develop an analytical Finite Element (FE) model for the T-joint systems of 2-inch fire protection piping system in hospitals subjected to seismic ground motions. In order to evaluate the FE models of the piping systems using OpenSees, two types of materials were used: 1) Steel 02 materials and 2) Pinching 4 materials. Results of the current study revealed that the nonlinear moment-rotation FE models for the threaded T-joint reconciled well with the experimental results in both FE material models. However, the system-level fragility determined from multiple nonlinear time history analyses at the threaded T-joint was slightly different. The system-level fragility at the T-joint, determined by Pinching 4 material was more conservative than that of using Steel 02 material in the piping system.

Keywords: fragility, t-joint, piping, leakage, sprinkler

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Authors: Tejeet Singh, Ishavneet Singh

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The present study focused on carrying out the creep analysis in an isotropic thick-walled composite cylindrical pressure vessel composed of aluminum matrix reinforced with silicon-carbide in particulate form. The creep behavior of the composite material has been described by the threshold stress based creep law. The values of stress exponent appearing in the creep law were selected as 3, 5 and 8. The constitutive equations were developed using well known von-Mises yield criteria. Models were developed to find out the distributions of creep stress and strain rate in thick-walled composite cylindrical pressure vessels under internal pressure. In order to obtain the stress distributions in the cylinder, the equilibrium equation of the continuum mechanics and the constitutive equations are solved together. It was observed that the radial stress, tangential stress and axial stress increases along with the radial distance. The cross-over was also obtained almost at the middle region of cylindrical vessel for tangential and axial stress for different values of stress exponent. The strain rates were also decreasing in nature along the entire radius.

Keywords: steady state creep, composite, cylinder, pressure

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Authors: Xiao-Dong Wang, Wei-Mon Yan

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The flow field design in the bipolar plates affects the performance of the proton exchange membrane (PEM) fuel cell. This work adopted a combined optimization procedure, including a simplified conjugate-gradient method and a completely three-dimensional, two-phase, non-isothermal fuel cell model, to look for optimal flow field design for a single serpentine fuel cell of size 9×9 mm with five channels. For the direct solution, the two-fluid method was adopted to incorporate the heat effects using energy equations for entire cells. The model assumes that the system is steady; the inlet reactants are ideal gases; the flow is laminar; and the porous layers such as the diffusion layer, catalyst layer and PEM are isotropic. The model includes continuity, momentum and species equations for gaseous species, liquid water transport equations in the channels, gas diffusion layers, and catalyst layers, water transport equation in the membrane, electron and proton transport equations. The Bulter-Volumer equation was used to describe electrochemical reactions in the catalyst layers. The cell output power density Pcell is maximized subjected to an optimal set of channel heights, H1-H5, and channel widths, W2-W5. The basic case with all channel heights and widths set at 1 mm yields a Pcell=7260 Wm-2. The optimal design displays a tapered characteristic for channels 1, 3 and 4, and a diverging characteristic in height for channels 2 and 5, producing a Pcell=8894 Wm-2, about 22.5% increment. The reduced channel heights of channels 2-4 significantly increase the sub-rib convection and widths for effectively removing liquid water and oxygen transport in gas diffusion layer. The final diverging channel minimizes the leakage of fuel to outlet via sub-rib convection from channel 4 to channel 5. Near-optimal design without huge loss in cell performance but is easily manufactured is tested. The use of a straight, final channel of 0.1 mm height has led to 7.37% power loss, while the design with all channel widths to be 1 mm with optimal channel heights obtained above yields only 1.68% loss of current density. The presence of a final, diverging channel has greater impact on cell performance than the fine adjustment of channel width at the simulation conditions set herein studied.

Keywords: optimization, flow field design, simplified conjugate-gradient method, serpentine flow field, sub-rib convection

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Authors: Gulshan Sachdeva, Ram Bilash

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In this paper, the exergy analysis of vapor absorption refrigeration system using LiBr-H2O as working fluid is carried out with the modified Gouy-Stodola approach rather than the classical Gouy-Stodola equation and effect of varying input parameters is also studied on the performance of the system. As the modified approach uses the concept of effective temperature, the mathematical expressions for effective temperature have been formulated and calculated for each component of the system. Various constraints and equations are used to develop program in EES to solve these equations. The main aim of this analysis is to determine the performance of the system and the components having major irreversible loss. Results show that exergy destruction rate is considerable in absorber and generator followed by evaporator and condenser. There is an increase in exergy destruction in generator, absorber and condenser and decrease in the evaporator by the modified approach as compared to the conventional approach. The value of exergy determined by the modified Gouy Stodola equation deviates maximum i.e. 26% in the generator as compared to the exergy calculated by the classical Gouy-Stodola method.

Keywords: exergy analysis, Gouy-Stodola, refrigeration, vapor absorption

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Authors: Carlos Teodoro, Oscar Bautista

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In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Seyyed Feisal Asbaghian Namin, Reza Pilafkan, Mahmood Kaffash Irzarahimi

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TThis paper considers vibration of single-layered graphene sheets using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source software, is used to obtain fundamental frequencies. On the other hand, governing equations are derived using nonlocal elasticity and first order shear deformation theory (FSDT) and solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in governing equations of motion by nonlocal parameter. The effect of different side lengths, boundary conditions and nonlocal parameter are inspected for aforementioned methods. Results are obtained from MD simulations is compared with those of the nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. The nonlocal parameter value is suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that the nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.

Keywords: graphene sheets, molecular dynamics simulations, fundamental frequencies, nonlocal elasticity theory, nonlocal parameter

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Authors: O. Rahli, N. Mimouni, R. Bennacer, K. Bouhadef

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This numerical study investigates the travelling wave’s appearance and the behavior of Poiseuille-Rayleigh-Benard (PRB) flow induced in 3D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The governing equations are discretized by using a control volume method with third order Quick scheme in approximating the advection terms. Simpler algorithm is used to handle coupling between the momentum and continuity equations. To avoid the excessively high computer time, full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For a broad range of dimensionless controlling parameters, the contribution of this work is to analyzing the flow regimes of the steady longitudinal thermoconvective rolls (noted R//) for both thermal and mass transfer (TSMC). The transition from the opposed volume forces to cooperating ones, considerably affects the birth and the development of the longitudinal rolls. The heat and mass transfers distribution are also examined.

Keywords: heat and mass transfer, mixed convection, poiseuille-rayleigh-benard flow, rectangular duct

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Authors: William Chung

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This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given.

Keywords: approximate subproblem, Dantzig-Wolfe decomposition, large-scale models, multiple subproblems

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Authors: Yanyan Zhang, Ziyu Diao, Zhentao Liu, Ruidong Yan

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The wear character of the main bearing is one of the critical indicators for the overhaul of an internal combustion engine, and the aim of this paper is to reveal the dynamic wear mechanism of the main bearings. A numerical simulation model combined multi-body dynamic equations of the engine, the average Reynolds equations of the bearing lubricant, asperity contact and wear model of the joint surfaces were established under typical operating conditions. The wear results were verified by experimental data, and then the influence of operating conditions, bearing clearance and cylinder pressure on the wear character of selected main bearings were analyzed. The results show that the contribution degree of different working conditions on the wear profile and depth of each bearing is obviously different, and the increase of joint clearance or cylinder pressure will accelerate the wear. The numerical model presented can be used to wear prognosis for joints and provide guidance for optimization design of sliding bearings.

Keywords: dynamic simulation, multi-body dynamics, sliding bearing, surface wear

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Authors: Mirza Mohibulla Baig, Imil Hamda Imran, Tri Bagus Susilo, Sami El Ferik

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The paper deals with system identification and control a nonlinear model of semi-autonomous underwater vehicle (UUV). The input-output data is first generated using the experimental values of the model parameters and then this data is used to compute the estimated parameter values. In this study, we use the semi-autonomous UUV LAURS model, which is developed by the Sensors and Actuators Laboratory in University of Sao Paolo. We applied three methods to identify the parameters: integral method, which is a classical least square method, recursive least square, and weighted recursive least square. In this paper, we also apply three different inputs (step input, sine wave input and random input) to each identification method. After the identification stage, we investigate the control performance of yaw motion of nonlinear semi-autonomous Unmanned Underwater Vehicle (UUV) using feedback linearization-based controller. In addition, we compare the performance of the control with an integral and a non-integral part along with state feedback. Finally, disturbance rejection and resilience of the controller is tested. The results demonstrate the ability of the system to recover from such fault.

Keywords: system identification, underwater vehicle, integral method, recursive least square, weighted recursive least square, feedback linearization, integral error

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Authors: Benselama Khadidja, El Meiche Noureddine

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This paper presents the effect of hybridization material on the variation of non-dimensional critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the Principle of Virtual Displacement; the formulation is based on a new function of shear deformation theory taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress-free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

Keywords: buckling, hybrid cross-ply laminates, Winkler and Pasternak, elastic foundation, two variables plate theory

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Authors: Moumita Sit, Chaitali Ray

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The present article deals with the free vibration analysis of hybrid laminated composite structures with initial stresses developed in the laminates. Generally initial stresses may be developed in the laminates by temperature and moisture effect. In this study, an eight noded isoparametric plate bending element has been used for the finite element analysis of composite plates. A numerical model has been developed to assess the geometric nonlinear response of composite plates based on higher order shear deformation theory (HSDT) considering the Green–Lagrange type nonlinearity. A computer code based on finite element method (FEM) has also been developed in MATLAB to perform the numerical calculations. To validate the accuracy of the proposed numerical model, the results obtained from the present study are compared with those available in published literature. Effects of the side to thickness ratio, different boundary conditions and initial stresses on the natural frequency of composite plates have been studied. The free vibration analysis of a hollow stiffened hybrid laminated panel has also been carried out considering initial stresses and presented as case study.

Keywords: geometric nonlinearity, higher order shear deformation theory (HSDT), hybrid composite laminate, the initial stress

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Authors: Mohammad Hossein Mohammadi Sanjani, Ashknaz Oraee, Arian Amirnia, Atena Taheri, Mohammadreza Arabi, Mahmud Fotuhi-Firuzabad

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Ferroresonance effects cause overvoltage in medium voltage transformers and isolators used in electrical networks. Ferroresonance effects are nonlinear and occur between the network capacitor and the nonlinear inductance of the voltage transformer during saturation. This phenomenon is unwanted for transformers since it causes overheating, introduction of high dynamic forces in primary coils, and rise of voltage in primary coils for the voltage transformer. Furthermore, it results in electrical and thermal failure of the transformer. Expansion of distribution lines, design of the transformer in smaller sizes, and the increase of harmonics in distribution networks result in an increase of ferroresonance. There is limited literature available to improve the effects of ferroresonance; therefore, optimizing its effects for voltage transformers is of great importance. In this study, comprehensive modeling of a medium voltage block-type voltage transformer is performed. In addition, a recent model is proposed to improve the performance of voltage transformers during the occurrence of ferroresonance using damping oscillations. Also, transformer design optimization is presented in this study to show further improvements in the performance of the voltage transformer. The recently proposed model is experimentally tested and verified on a medium voltage transformer in the laboratory, and simulation results show a large reduction of the effects of ferroresonance.

Keywords: optimization, voltage transformer, ferroresonance, modeling, damper

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Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen, , Jing Bai

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Piezoelectric laminated smart structures can be subjected to the strong driving electric field, which may result in large displacements and rotations. In one hand, piezoelectric materials usually behave very significant material nonlinear effects under strong electric fields. On the other hand, thin-walled structures undergoing large displacements and rotations exist nonnegligible geometric nonlinearity. In order to give a precise prediction of piezo laminated smart structures under the large electric field, this paper develops a finite element (FE) model accounting for material nonlinearity (piezoelectric part) and geometric nonlinearity based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is first validated by both experimental and numerical examples from the literature. Afterwards, it is applied to simulate for plate and shell structures with multiple piezoelectric patches under the strong applied electric field. From the simulation results, it shows that large discrepancies occur between linear and nonlinear predictions for piezoelectric laminated structures driving at the strong electric field. Therefore, both material and geometric nonlinearities should be taken into account for piezoelectric structures under strong electric.

Keywords: piezoelectric smart structures, finite element analysis, geometric nonlinearity, electroelastic material nonlinearities

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Authors: Vimal Kumar Chouksey, S. P. Sharma

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This paper deals with theoretical analysis of performance of solar air collector having its duct packed with blackened wire screen matrices. The heat transfer equations for two-dimensional fully developed fluid flows under quasi-steady-state conditions have been developed in order to analyze the effect of bed depth on performance. A computer programme is developed in C++ language to estimate the temperature rise of entering air for evaluation of performance by solving the governing equations numerically using relevant correlations for heat transfer coefficient for packed bed systems. Results of air temperature rise and thermal efficiency obtained from the analysis have been compared with available experimental results and results have been found fairly in closed agreement. It has been found that there is considerable enhancement in performance with packed bed collector upto a certain total bed depth. Effect of total bed depth on efficiency show that there is an upper limiting value of total bed depth beyond which the thermal efficiency begins to fall again and this type of characteristics behavior is observed at all mass flow rate.

Keywords: plane collector, solar air heater, solar energy, wire screen packed bed

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Authors: Ahmad Akrad, Rabia Sehab, Fadi Alyoussef

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Nowadays, induction machines are widely used in industry thankful to their advantages comparing to other technologies. Indeed, there is a big demand because of their reliability, robustness and cost. The objective of this paper is to deal with diagnosis, detection and isolation of faults in a three-phase induction machine. Among the faults, Inter-turn short-circuit fault (ITSC), current sensors fault and single-phase open circuit fault are selected to deal with. However, a fault detection method is suggested using residual errors generated by the root mean square (RMS) of phase currents. The application of this method is based on an asymmetric nonlinear model of Induction Machine considering the winding fault of the three axes frame state space. In addition, current sensor redundancy and sensor fault detection and isolation (FDI) are adopted to ensure safety operation of induction machine drive. Finally, a validation is carried out by simulation in healthy and faulty operation modes to show the benefit of the proposed method to detect and to locate with, a high reliability, the three types of faults.

Keywords: induction machine, asymmetric nonlinear model, fault diagnosis, inter-turn short-circuit fault, root mean square, current sensor fault, fault detection and isolation

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Authors: Juan José Mesas, Luis Sainz

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The motivation for the development of this paper lies in the need for energy networks to reduce losses, improve performance, optimize their operation and try to benefit from the interconnection capacity with other networks enabled for other energy carriers. These interconnections generate interdependencies between some energy networks and others, which requires suitable models and methods for their analysis. Traditionally, the modeling and study of energy networks have been carried out independently for each energy carrier. Thus, there are well-established models and methods for the steady-state analysis of electrical networks, gas networks, and thermal networks separately. What is intended is to extend and combine them adequately to be able to face in an integrated way the steady-state analysis of networks with multiple energy carriers. Firstly, the added value of multi-energy networks, their operation, and the basic principles that characterize them are explained. In addition, two current aspects of great relevance are exposed: the storage technologies and the coupling elements used to interconnect one energy network with another. Secondly, the characteristic equations of the different energy networks necessary to carry out the steady-state analysis are detailed. The electrical network, the natural gas network, and the thermal network of heat and cold are considered in this paper. After the presentation of the equations, a particular case of the steady-state analysis of a specific multi-energy network is studied. This network is represented graphically, the interconnections between the different energy carriers are described, their technical data are exposed and the equations that have previously been presented theoretically are formulated and developed. Finally, the two iterative numerical resolution methods considered in this paper are presented, as well as the resolution procedure and the results obtained. The pros and cons of the application of both methods are explained. It is verified that the results obtained for the electrical network (voltages in modulus and angle), the natural gas network (pressures), and the thermal network (mass flows and temperatures) are correct since they comply with the distribution, operation, consumption and technical characteristics of the multi-energy network under study.

Keywords: coupling elements, energy carriers, multi-energy networks, steady-state analysis

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Authors: A. Zaidi, F. Khelifi, R. Masmoudi, M. Bouhicha

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5 In order to eradicate the degradation of reinforced concrete structures due to the steel corrosion, professionals in constructions suggest using fiber reinforced polymers (FRP) for their excellent properties. Nevertheless, high temperatures may affect the bond between FRP bar and concrete, and consequently the serviceability of FRP-reinforced concrete structures. This paper presents a nonlinear numerical investigation using ADINA software to investigate the effect of the spacing between glass FRP (GFRP) bars embedded in concrete on circumferential thermal deformations and the distribution of radial thermal cracks in reinforced concrete beams submitted to high temperature variations up to 60 °C for asymmetrical problems. The thermal deformations predicted from nonlinear finite elements model, at the FRP bar/concrete interface and at the external surface of concrete cover, were established as a function of the ratio of concrete cover thickness to FRP bar diameter (c/d_b) and the ratio of spacing between FRP bars in concrete to FRP bar diameter (e/d_b). Numerical results show that the circumferential thermal deformations at the external surface of concrete cover are linear until cracking thermal load varied from 32 to 55 °C corresponding to the ratio of e/d_b varied from 1.3 to 2.3, respectively. However, for ratios e/d_b >2.3 and c/d_b >1.6, the thermal deformations at the external surface of concrete cover exhibit linear behavior without any cracks observed on the specified surface. The numerical results are compared to those obtained from analytical models validated by experimental tests.

Keywords: concrete beam, FRP bars, spacing effect, thermal deformation

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Authors: A. Falavand Jozaei, A. Ghafouri

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Operation enhancement in an air cooler (heat exchanger) depends on the rate of heat transfer, and pressure drop. In this paper, for a given heat duty, study of the effects of FPI (fin per inch) and fin type (circular and hexagonal fins) on two parameters mentioned above is considered in an air cooler in Iran, Arvand petrochemical. A program in EES (Engineering Equations Solver) software moreover, Aspen B-JAC and HTFS+ software are used for this purpose to solve governing equations. At first the simulated results obtained from this program is compared to the experimental data for two cases of FPI. The effects of FPI from 3 to 15 over heat transfer (Q) to pressure drop ratio (Q/Δp ratio). This ratio is one of the main parameters in design, rating, and simulation heat exchangers. The results show that heat transfer (Q) and pressure drop increase with increasing FPI (fin per inch) steadily, and the Q/Δp ratio increases to FPI = 12 (for circular fins about 47% and for hexagonal fins about 69%) and then decreased gradually to FPI = 15 (for circular fins about 5% and for hexagonal fins about 8%), and Q/Δp ratio is maximum at FPI = 12. The FPI value selection between 8 and 12 obtained as a result to optimum heat transfer to pressure drop ratio. Also by contrast, between circular and hexagonal fins results, the Q/Δp ratio of hexagonal fins more than Q/Δp ratio of circular fins for FPI between 8 and 12 (optimum FPI).

Keywords: air cooler, circular and hexagonal fins, fin per inch, heat transfer and pressure drop

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Authors: Pedro A. Marques, Francisco Monteiro, Alessandra Zumbo, Alessia Simonini, Miguel A. Mendez

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Cryogenic fuels such as Liquid Hydrogen (LH₂) must be transported and stored at extremely low temperatures. Without expensive active cooling solutions, preventing fuel boil-off over time is impossible. Hence, one must resort to venting systems at the cost of significant energy and fuel mass loss. These losses increase significantly in propellant tanks installed on vehicles, as the presence of external accelerations induces sloshing. Sloshing increases heat and mass transfer rates and leads to significant pressure oscillations, which might further trigger propellant venting. To make LH₂ economically viable, it is essential to minimize these factors by using advanced control techniques. However, these require accurate modelling and a full understanding of the tank's thermodynamics. The present research aims to implement a simple thermodynamic model capable of predicting the state of a cryogenic fuel tank under different operating conditions (i.e., filling, pressurization, fuel extraction, long-term storage, and sloshing). Since this model relies on a set of closure parameters to drive the system's transient response, it must be calibrated using experimental or numerical data. This work focuses on the former approach, wherein the model is calibrated through an experimental campaign carried out on a reduced-scale model of a cryogenic tank. The thermodynamic model of the system is composed of three control volumes: the ullage, the liquid, and the insulating walls. Under this lumped formulation, the governing equations are derived from energy and mass balances in each region, with mass-averaged properties assigned to each of them. The gas-liquid interface is treated as an infinitesimally thin region across which both phases can exchange mass and heat. This results in a coupled system of ordinary differential equations, which must be closed with heat and mass transfer coefficients between each control volume. These parameters are linked to the system evolution via empirical relations derived from different operating regimes of the tank. The derivation of these relations is carried out using an inverse method to find the optimal relations that allow the model to reproduce the available data. This approach extends classic system identification methods beyond linear dynamical systems via a nonlinear optimization step. Thanks to the data-driven assimilation of the closure problem, the resulting model accurately predicts the evolution of the tank's thermodynamics at a negligible computational cost. The lumped model can thus be easily integrated with other submodels to perform complete system simulations in real time. Moreover, by setting the model in a dimensionless form, a scaling analysis allowed us to relate the tested configurations to a representative full-size tank for naval applications. It was thus possible to compare the relative importance of different transport phenomena between the laboratory model and the full-size prototype among the different operating regimes.

Keywords: destratification, hydrogen, modeling, pressure-drop, pressurization, sloshing, thermodynamics

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Authors: Mohammed Ali Hjaji, A.K. El-Senussi, Said H. Eshtewi

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The flexural dynamic response of symmetric laminated composite beams subjected to general transverse harmonic forces is investigated. The dynamic equations of motion and associated boundary conditions based on the first order shear deformation are derived through the use of Hamilton’s principle. The influences of shear deformation, rotary inertia, Poisson’s ratio and fibre orientation are incorporated in the present formulation. The resulting governing flexural equations for symmetric composite Timoshenko beams are exactly solved and the closed form solutions for steady state flexural response are then obtained for cantilever and simply supported boundary conditions. The applicability of the analytical closed-form solution is demonstrated via several examples with various transverse harmonic loads and symmetric cross-ply and angle-ply laminates. Results based on the present solution are assessed and validated against other well established finite element solutions and exact solutions available in the literature.

Keywords: analytical solution, flexural response, harmonic forces, symmetric laminated beams, steady state response

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Authors: Yuanhao Gao, Pin Lin, Kees Weijer

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In this paper, we will determine the external body force distribution with analysis of stokes fluid motion using mathematical modelling and numerical approaching. The body force distribution is regarded as the unknown variable and could be determined by the idea of optimal control theory. The Stokes flow motion and its velocity are generated by given forces in a unit square domain. A regularized objective functional is built to match the numerical result of flow velocity with the generated velocity data. So that the force distribution could be determined by minimizing the value of objective functional, which is also the difference between the numerical and experimental velocity. Then after utilizing the Lagrange multiplier method, some partial differential equations are formulated consisting the optimal control system to solve. Finite element method and conjugate gradient method are used to discretize equations and deduce the iterative expression of target body force to compute the velocity numerically and body force distribution. Programming environment FreeFEM++ supports the implementation of this model.

Keywords: optimal control model, Stokes equation, finite element method, conjugate gradient method

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Authors: Ayola D. N. Jayamaha, Gihan V. Dias, Surangika Ranathunga

Abstract:

Currently there are lot of educational tools designed for mathematics. Open source software such as GeoGebra and Octave are bulky in their architectural structure. In addition, there is MathLab software, which facilitates much more than what we ask for. Many of the computer aided online grading and assessment tools require integrating editors to their software. However, there are not exist suitable editors that cater for all their needs in editing equations and geometrical diagrams and graphs. Some of the existing software for editing equations is Alfred’s Equation Editor, Codecogs, DragMath, Maple, MathDox, MathJax, MathMagic, MathFlow, Math-o-mir, Microsoft Equation Editor, MiraiMath, OpenOffice, WIRIS Editor and MyScript. Some of them are commercial, open source, supports handwriting recognition, mobile apps, renders MathML/LaTeX, Flash / Web based and javascript display engines. Some of the diagram editors are GeoKone.NET, Tabulae, Cinderella 1.4, MyScript, Dia, Draw2D touch, Gliffy, GeoGebra, Flowchart, Jgraph, JointJS, J painter Online diagram editor and 2D sketcher. All these software are open source except for MyScript and can be used for editing mathematical diagrams. However, they do not fully cater the needs of a typical computer aided assessment tool or Educational Platform for Mathematics. This solution provides a Web based, lightweight, easy to implement and integrate solution of an html5 canvas that renders on all of the modern web browsers. The scope of the project is an editor that covers equations and mathematical diagrams and drawings on the O/L Mathematical Exam Papers in Sri Lanka. Using the tool the students can enter any equation to the system which can be on an online remote learning platform. The users can also create and edit geometrical drawings, graphs and do geometrical constructions that require only Compass and Ruler from the Editing Interface provided by the Software. The special feature of this software is the geometrical constructions. It allows the users to create geometrical constructions such as angle bisectors, perpendicular lines, angles of 600 and perpendicular bisectors. The tool correctly imitates the functioning of rulers and compasses to create the required geometrical construction. Therefore, the users are able to do geometrical drawings on the computer successfully and we have a digital format of the geometrical drawing for further processing. Secondly, we can create and edit Venn Diagrams, color them and label them. In addition, the students can draw probability tree diagrams and compound probability outcome grids. They can label and mark regions within the grids. Thirdly, students can draw graphs (1st order and 2nd order). They can mark points on a graph paper and the system connects the dots to draw the graph. Further students are able to draw standard shapes such as circles and rectangles by selecting points on a grid or entering the parametric values.

Keywords: geometrical drawings, html5 canvas, mathematical equations, toolbox

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Authors: Medine Demir, Volker John

Abstract:

Fluid equations in a rotating frame of reference have a broad class of important applications in meteorology and oceanography, especially in the large-scale flows considered in ocean and atmosphere, as well as many physical and industrial applications. The Coriolis and the centripetal forces, resulting from the rotation of the earth, play a crucial role in such systems. For such applications it may be required to solve the system in complex three-dimensional geometries. In recent years, the Navier--Stokes equations in a rotating frame have been investigated in a number of papers using the classical inf-sup stable mixed methods, like Taylor-Hood pairs, to contribute to the analysis and the accurate and efficient numerical simulation. Numerical analysis reveals that these classical methods introduce a pressure-dependent contribution in the velocity error bounds that is proportional to some inverse power of the viscosity. Hence, these methods are optimally convergent but small velocity errors might not be achieved for complicated pressures and small viscosity coefficients. Several approaches have been proposed for improving the pressure-robustness of pairs of finite element spaces. In this contribution, a pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. However, this approach might come with a modification of the meshes, like the use of barycentric-refined grids in case of Scott--Vogelius pairs. However, this strategy requires the finite element code to have control on the mesh generator which is not realistic in many engineering applications and might also be in conflict with the solver for the linear system. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples illustrate the theoretical results. The idea of pressure-robust method could be cast on different types of flow problems which would be considered as future studies. As another future research direction, to avoid a modification of the mesh, one may use a very simple parameter-dependent modification of the Scott-Vogelius element, the pressure-wired Stokes element, such that the inf-sup constant is independent of nearly-singular vertices.

Keywords: navier-stokes equations in a rotating frame of refence, coriolis force, pressure-robust error estimate, scott-vogelius pairs of finite element spaces

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Authors: Mohamed A. Shanan, Ashraf H. El-Zanaty, Kamal G. Metwally

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This paper presents the effect of concrete compressive strength and rectangularity ratio on strength and ductility of normal and high strength reinforced concrete columns confined with transverse steel under axial compressive loading. Nineteen normal strength concrete rectangular columns with different variables tested in this research were used to study the effect of concrete compressive strength and rectangularity ratio on strength and ductility of columns. The paper also presents a nonlinear finite element analysis for these specimens and another twenty high strength concrete square columns tested by other researchers using ANSYS 15 finite element software. The results indicate that the axial force – axial strain relationship obtained from the analytical model using ANSYS are in good agreement with the experimental data. The comparison shows that the ANSYS is capable of modeling and predicting the actual nonlinear behavior of confined normal and high-strength concrete columns under concentric loading. The maximum applied load and the maximum strain have also been confirmed to be satisfactory. Depending on this agreement between the experimental and analytical results, a parametric numerical study was conducted by ANSYS 15 to clarify and evaluate the effect of each variable on strength and ductility of the columns.

Keywords: ANSYS, concrete compressive strength effect, ductility, rectangularity ratio, strength

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Authors: Bandari Shankar, Yohannes Yirga

Abstract:

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement

Keywords: unsteady, heat and mass transfer, manetohydrodynamics, nanofluid, non-uniform heat source/sink, stretching sheet

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Authors: Abdelkarim M. Ertiame, D. W. Yu, D. L. Yu, J. B. Gomm

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In this paper, a new robust fault detection and isolation (FDI) scheme is developed to monitor a multivariable nonlinear chemical process called the Chylla-Haase polymerization reactor when it is under the cascade PI control. The scheme employs a radial basis function neural network (RBFNN) in an independent mode to model the process dynamics and using the weighted sum-squared prediction error as the residual. The recursive orthogonal Least Squares algorithm (ROLS) is employed to train the model to overcome the training difficulty of the independent mode of the network. Then, another RBFNN is used as a fault classifier to isolate faults from different features involved in the residual vector. The several actuator and sensor faults are simulated in a nonlinear simulation of the reactor in Simulink. The scheme is used to detect and isolate the faults on-line. The simulation results show the effectiveness of the scheme even the process is subjected to disturbances and uncertainties including significant changes in the monomer feed rate, fouling factor, impurity factor, ambient temperature and measurement noise. The simulation results are presented to illustrate the effectiveness and robustness of the proposed method.

Keywords: Robust fault detection, cascade control, independent RBF model, RBF neural networks, Chylla-Haase reactor, FDI under closed-loop control

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Authors: Musa Auwal Mamman, S. G. Isa

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This study was carried out in order to investigate the effectiveness of GeoGebra software in teaching and learning of linear and quadratic equations amongst senior secondary school students in Fagge Local Government Area, Kano State–Nigeria. Five research items were raised in objectives, research questions and hypotheses respectively. A random sampling method was used in selecting 398 students from a population of 2098 of SS2 students. The experimental group was taught using the GeoGebra software while the control group was taught using the conventional teaching method. The instrument used for the study was the mathematics performance test (MPT) which was administered at the beginning and at the end of the study. The results of the study revealed that students taught with GeoGebra software (experimental group) performed better than students taught with traditional teaching method. The t- test was used to analyze the data obtained from the study.

Keywords: GeoGebra Software, mathematics performance, random sampling, mathematics teaching

Procedia PDF Downloads 234

Authors: Arvan Prakash Ankitha, Madasamy Arockiasamy

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The increasing demand for adopting pile foundations in bridgeshas pointed towardsthe need to constantly improve the existing analytical techniques for better understanding of the behavior of such foundation systems. This study presents a simplistic approach using the energy-based method to assess the displacement responses of piles subjected to general loading conditions: Axial Load, Lateral Load, and a Bending Moment. The governing differential equations and the boundary conditions for a bridge pile embedded in multi-layered soil strata subjected to the general loading conditions are obtained using the Hamilton’s principle employing variational principles and minimization of energies. The soil non-linearity has been incorporated through simple constitutive relationships that account for degradation of soil moduli with increasing strain values.A simple power law based on published literature is used where the soil is assumed to be nonlinear-elastic and perfectly plastic. A Tresca yield surface is assumed to develop the soil stiffness variation with different strain levels that defines the non-linearity of the soil strata. This numerical technique has been applied to a pile foundation in a two - layered soil strata for a pier supporting the bridge and solved using the software MATLAB R2019a. The analysis yields the bridge pile displacements at any depth along the length of the pile. The results of the analysis are in good agreement with the published field data and the three-dimensional finite element analysis results performed using the software ANSYS 2019R3. The methodology can be extended to study the response of the multi-strata soil supporting group piles underneath the bridge piers.

Keywords: pile foundations, deep foundations, multilayer soil strata, energy based method

Procedia PDF Downloads 117

Authors: Libo Jiang, Huan Li, Rongling Wu

Abstract:

Ordinary differentiation equations (ODE) have proven to be powerful for reconstructing precise and informative gene regulatory networks (GRNs) from dynamic gene expression data. However, joint modeling and analysis of all genes, essential for the systematical characterization of genetic interactions, are challenging due to high dimensionality and a complex pattern of genetic regulation including activation, repression, and antitermination. Here, we address these challenges by unifying variable selection and game theory through ODE. Each gene within a GRN is co-expressed with its partner genes in a way like a game of multiple players, each of which tends to choose an optimal strategy to maximize its “fitness” across the whole network. Based on this unifying theory, we designed and conducted a real experiment to infer salt tolerance-related GRNs for Euphrates poplar, a hero tree that can grow in the saline desert. The pattern and magnitude of interactions between several hub genes within these GRNs were found to determine the capacity of Euphrates poplar to resist to saline stress.

Keywords: gene regulatory network, ordinary differential equation, game theory, LASSO, saline resistance

Procedia PDF Downloads 624